16. Q16
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Similar Question 1
<p>Find the measure of <code class='latex inline'>\angle A</code>, to the nearest degree.</p><img src="/qimages/9425" />
Similar Question 2
<p> Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65419" />
Similar Question 3
<p>In a right triangle, the side opposite the <code class='latex inline'> 53^{\circ} </code> angle is <code class='latex inline'> 4 \mathrm{~cm} </code> long. How long is the side adjacent to the <code class='latex inline'> 53^{\circ} </code> angle, to the nearest centimetre?</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65222" />
<p>Find x, to the nearest tenth of a unit.</p><img src="/qimages/9427" />
<p>Solve the triangle. Round lengths to the nearest unit and angle measures to the nearest degree.</p><img src="/qimages/9431" />
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth.</p><img src="/qimages/22851" />
<p>BACKPACKS Ramón has a rolling backpack that is <code class='latex inline'>\displaystyle 3 \frac{3}{4} </code> feet tall when the handle is extended. When he is pulling the backpack, Ramon&#39;s hand is 3 feet from the ground. What angle does his backpack make with the floor? Round to the nearest degree.</p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin Q = 0.2315</code></p>
<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/2380" />
<p>Draw two different right triangles for which <code class='latex inline'>\tan\theta=1</code>. Determine the measurements of all the sides and angles. Then compare the two triangles.</p>
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65313" />
<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>AB = 5 cm</code>, <code class='latex inline'>AC = 8 cm</code>, and <code class='latex inline'>\angle B = 90^{\circ}</code>. Solve <code class='latex inline'>\triangle ABC</code>.</p>
<p>Find <code class='latex inline'> \angle \mathrm{Q} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos Q=\frac{5}{9} </code></p>
<p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22784" />
<p>Find the three primary trigonometric ratios for <code class='latex inline'>\angle A</code>, to four decimal places.</p><img src="/qimages/22862" />
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6957" />
<p>In a right</p><p>triangle, the hypotenuse</p><p>is 5 in. long, and the side</p><p>opposite <code class='latex inline'>\displaystyle \angle A </code> is <code class='latex inline'>\displaystyle 4.5 </code> in. long. A student found the</p><p>measure of <code class='latex inline'>\displaystyle \angle A </code> as <code class='latex inline'> \displaystyle sin(0.9) = 0.0157 </code></p><p> Describe and correct the student&#39;s error.</p>
<p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6767" />
<p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. <code class='latex inline'>\displaystyle 8,15,17 </code></p>
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2383" />
<p>Solve each triangle. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.</p><img src="/qimages/22891" />
<p>Find the measure of each angle, to the nearest degree.</p><p>tan Y = <code class='latex inline'>\dfrac{5}{12}</code></p>
<ol> <li>a) Evaluate <code class='latex inline'>\displaystyle \sin 39^{\circ} </code> with a calculator. Round your answer to the nearest thousandth. b) Use the diagram to write the ratio represented by your answer to part a).</li> </ol> <p>c) What is the length of <code class='latex inline'>\displaystyle a </code> in terms of <code class='latex inline'>\displaystyle c </code> ? d) What is the length of <code class='latex inline'>\displaystyle c </code> in terms of <code class='latex inline'>\displaystyle a </code> ?</p><img src="/qimages/65327" />
<p>Predict the order, from tallest to shortest, of these famous landmarks_ Then use the given information to determine the actual heights to the nearest metre.</p> <ul> <li>Eiffel Tower, Paris, France 68 m from the base, the angle of elevation to the top is <code class='latex inline'>78^o</code></li> </ul>
<p>Find <code class='latex inline'> \angle W </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan W=\frac{6}{7} </code></p>
<p>Find the tangent of the greater acute angle in a triangle with side lengths of 3,4 , and 5 centimeters.</p>
<p>Predict the order, from tallest to shortest, of these famous landmarks_ Then use the given information to determine the actual heights to the nearest metre.</p> <ul> <li>Big Ben’s clock tower, London, England 81 m from the base, the angle of elevation is tower is 81 m with an angle of elevation of <code class='latex inline'>50^o</code></li> </ul>
<p>For <code class='latex inline'>\displaystyle \triangle F G H </code> and <code class='latex inline'>\displaystyle \triangle L M N </code>, find the value of each expression.</p><img src="/qimages/60806" /><p><code class='latex inline'>\displaystyle \sin F </code></p>
<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>\angle C = 90^o</code>. If <code class='latex inline'>\sin A = 0.5</code>, what is the measure of <code class='latex inline'>\angle B</code>?</p>
<p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. </p><p><code class='latex inline'>\displaystyle 18,24,30 </code></p>
<p>Find each trigonometric ratio for angle <code class='latex inline'>A</code> in the triangle at the right. </p><img src="/qimages/60797" /><p><code class='latex inline'>\displaystyle \sin A </code></p>
<p>A road sign shows that a hill has a grade of 8%. What is the angle of inclination of the hill, to the nearest tenth of a degree?</p>
<p>The CN Tower is 553 m tall. From a position on one of the Toronto u Islands 1.13 km away from the base of the tower, determine the angle of elevation, to the nearest degree, to the top of the tower. Assume that your eyes are 1.5 m above ground.</p><img src="/qimages/2285" />
<p>When a road has a <code class='latex inline'>10\%</code> gradient, it means that the road rises <code class='latex inline'>10</code> In for every <code class='latex inline'>100</code> m of horizontal distance travelled. What is the angle of inclination of the road, to the nearest degree?</p>
<p>Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65415" />
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\displaystyle \begin{array}{llll} &a) & \cos \theta = 0.4481 &b) & \cos \theta = 0.6329\\ &c) & \cos C = \frac{5}{11} &d) & \cos S = 0.3432\\ &e) & \cos \theta = 0.8871 &f) & \cos A = \frac{3}{14}\\ &g) & \cos \theta = \frac{1}{6} &h) & \cos \theta = 0.6215 \\ &i) & \cos X = \frac{15}{16} &j) & \cos \theta = 0.0193 \\ &k) & \cos V = 0 &l) & \cos J = \frac{1}{2} \\ \end{array} </code></p>
<p>A telephone pole is secured at its top with a guy wire, as shown. The guy wire makes an angle of <code class='latex inline'>70</code>° with the ground and is secured <code class='latex inline'>5.6</code> m from the bottom of the pole. Find the height of the telephone pole.</p> <ul> <li>Find the length of the guy wire using two different methods.</li> </ul> <img src="/qimages/1618" />
<p> Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65429" />
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65219" />
<p>Are all squares similar? Justify your answer.</p>
<p>An isosceles triangle has sides that measure 4 cm, 10 cm, and 10 cm. What is the area of the triangle?</p><p>A. 38 <code class='latex inline'>cm^2</code></p><p>B. 10 <code class='latex inline'>cm^2</code></p><p>C. 25 <code class='latex inline'>cm^2</code></p><p>D. 20 <code class='latex inline'>cm^2</code></p>
<p>a) Use the sine law to find <code class='latex inline'> x </code> , to the nearest tenth.</p><p>b) Use the sine ratio to find <code class='latex inline'> x </code> , to the nearest tenth.</p><p>c) Explain why the two methods are equivalent in a right triangle.</p><img src="/qimages/66331" />
<p>Find the measure of <code class='latex inline'>\angle A</code>, to the nearest degree.</p><img src="/qimages/9425" />
<p>Find the three primary trigonometric ratios for <code class='latex inline'>\angle A</code>, to four decimal places.</p><img src="/qimages/22861" />
<p>State all the primary trigonometric ratios for <code class='latex inline'>\angle D</code> and <code class='latex inline'>\angle F</code>. Then determine <code class='latex inline'>\angle A</code> and <code class='latex inline'>\angle D</code> to the nearest degree.</p><img src="/qimages/2278" />
<p>Solve each triangle. Round each length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/165159" />
<p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>. Round to the nearest tenth.</p><img src="/qimages/104263" />
<p>Find the measures of both acute angles in each triangle to the nearest degree.</p><img src="/qimages/22848" />
<p>If in <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>AC = b, BC = a</code>, and <code class='latex inline'>\angle C</code> is known, then the area of <code class='latex inline'>\triangle ABC = \frac{1}{2}ab \sin C</code>. Show that this formula is true.</p>
<p>Decide whether each statement is true or false. Justify your decision.</p><p> <code class='latex inline'>\cos\alpha \doteq 0.8929</code></p><img src="/qimages/1023" />
<p> A perpendicular <code class='latex inline'>\overline{AP}</code> is drawn to base <code class='latex inline'>\overline{BC}</code> in <code class='latex inline'>\triangle ABC</code>. If <code class='latex inline'>\overline{AP} = 12, \overline{BP} = 5</code>, and <code class='latex inline'>\overline{PC} = 25</code>, determine if <code class='latex inline'>\triangle ABC</code> contains a right angle. Leave your answer in exact value.</p><img src="/qimages/2358" />
<p>Determine the length of the indicated side or the measure of the indicated angle.</p><img src="/qimages/6193" />
<p>Solve each triangle.</p><img src="/qimages/6762" />
<p>Determine all unknown sides to the nearest unit and all unknown interior a angles to the nearest degree.</p><img src="/qimages/2282" />
<p>Solve each triangle. Round each length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/165160" />
<p> Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65427" />
<p>Solve for <code class='latex inline'>x</code>, and express your answer to one decimal place.</p><p><code class='latex inline'>\tan80^{\circ}=\displaystyle{\frac{12}{x}}</code></p>
<p> Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65426" />
<p>Do you need to use a primary trigonometric ratio to determine the measure of <code class='latex inline'>y</code>? Explain.</p><img src="/qimages/1024" />
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 25^{\circ}</code></p>
<p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22842" />
<p>Graphing Calculator For each angle <code class='latex inline'>\displaystyle \theta </code>, find the values of <code class='latex inline'>\displaystyle \cos \theta </code> and <code class='latex inline'>\displaystyle \sin \theta . </code> Round your answers to the nearest hundredth.</p><p><code class='latex inline'>\displaystyle -95^{\circ} </code></p>
<p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{1}{2} </code></p>
<p>Three blood stains from a victim are of the aircraft, so that the beams will meet shown. The point of convergence, C, has been found by extrapolating the directions of these stains along the floor. The origin of the blow, O, is some height above C.</p><img src="/qimages/5596" /><p>Forensic analysis of Stain 1 provides the following data.</p> <ul> <li>Length of bloodstain: 4.2 cm</li> <li>Width of bloodstain: 2.6 cm</li> <li>Distance from point of convergence: 2.1</li> </ul> <p>Determine the height at which the blow struck the victim.</p>
<p>Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.</p><img src="/qimages/104243" />
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/22882" />
<p>Predict the order, from tallest to shortest, of these famous landmarks_ Then use the given information to determine the actual heights to the nearest metre.</p> <ul> <li>Empire State Building, New York, New York 267 m from the base, the angle of elevation to the top is 5<code class='latex inline'>58^o</code></li> </ul>
<p>Two angles in a triangle measure 54° and 38°. The longest side of the triangle is 24 cm longer than the shortest side. Calculate the length, to the nearest centimetre, of all three sides.</p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a unit.</p><img src="/qimages/5483" />
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6749" />
<p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6768" />
<p>Find the measure of <code class='latex inline'>\angle A</code>, to the nearest degree.</p><img src="/qimages/5471" />
<p>For what value of <code class='latex inline'>\theta</code> does <code class='latex inline'>\sin\theta=\cos\theta</code>? Include a diagram in your answer.</p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a unit.</p><img src="/qimages/5481" />
<p>A set of stairs in a cottage has a slope of <code class='latex inline'>\dfrac{7}{9}</code>. What angle do the stairs make with the horizontal, to the nearest degree?</p>
<p>To use an extension ladder safely, the base must be 1 m out from the wall for every 2 m of vertical height.</p><p>a) What is the maximum angle of elevation, to the nearest degree, to the top of the ladder?</p><p>b) If the ladder is extended to 4.72 m in length, how high can it safely reach? Round your answer to the nearest hundredth of a metre.</p><p>c) How far out from the wall does a 5.9 m ladder need to be? Round your answer to the nearest tenth of a metre.</p>
<p>Determine x to one decimal place.</p><p><code class='latex inline'>\displaystyle \tan 46^o = \frac{x}{14.2} </code></p>
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth.</p><img src="/qimages/22854" />
<p>Find <code class='latex inline'> \angle \mathrm{Q} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos \mathrm{Q}=\frac{1}{6} </code></p>
<p>Determine all unknown sides to the nearest unit and all unknown interior a angles to the nearest degree.</p><img src="/qimages/2283" />
<p>When poured into a pile, gravel will naturally form a cylindrical cone with a slope of approximately <code class='latex inline'>34^o</code>. If a construction foreman has room only for a pile that is 85 m in diameter, how tall, to the nearest metre, will the pile be?</p>
<p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/22864" />
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 45^{\circ} </code></p>
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6492" />
<p>Use a special right triangle to express each trigonometric ratio as a fraction and as a decimal to the nearest hundredth. <code class='latex inline'>\displaystyle \cos 60^{\circ} </code></p>
<p> Find tan <code class='latex inline'> A </code> and tan <code class='latex inline'> C </code> in each triangle. Round answers to the nearest thousandth, if necessary</p><img src="/qimages/65176" />
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6962" />
<p>A parallelogram has adjacent sides that are 11.0 cm and 15.0 cm long. The angle between these sides is 50°. Determine the length of the shorter diagonal.</p>
<p>Elise drew a diagram of her triangular yard. She wants to cover her yard with sod. Explain how you could calculate the cost, if sod costs $1.50/m<code class='latex inline'>^2</code>.</p><img src="/qimages/1052" /> <p>A tree is splintered by lightning 2 m up its trunk, so that the top part of the tree touches the ground. The angle the top of the tree forms with the ground is 70°. Before it was splintered, how tall was the tree, to the nearest tenth of a metre?</p><img src="/qimages/6757" /> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65305" /> <p>To avoid damaging a vital organ, a surgeon will fire a laser at an angle to the patient’s skin, to reach a cyst (an abnormal growth). The cyst is <code class='latex inline'>8.2</code> cm directly below the skin, and the laser is positioned at a distance of <code class='latex inline'>9.6</code> cm away in order to miss the Vital organ, as shown.</p><img src="/qimages/5474" /><p>At what angle, <code class='latex inline'>\theta</code>, should the surgeon position the laser with respect to the skin&#39;s surface?</p> <p>Draw two rectangles that are congruent.</p> <p>Solve each proportion. Round to the nearest tenth if necessary.</p><p><code class='latex inline'>\displaystyle 0.05 x=13 </code></p> <p>Evaluate the following, to four decimal places.</p><p>a) <code class='latex inline'>\tan 29^o</code></p><p>b) <code class='latex inline'>\cos 78^o</code></p><p>c) <code class='latex inline'>\sin 90^o</code></p><p>d) <code class='latex inline'>\sin 45^o</code></p><p>e) <code class='latex inline'>\cos 45^o</code></p><p>f) <code class='latex inline'>\tan 85^o</code></p> <p>Solve the triangle. Round lengths to the nearest unit and angle measures to the nearest degree.</p><img src="/qimages/9430" /> <p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{3}{4} </code></p> <p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.998 </code></p> <p>Use geometric reasoning to show that the angle of impact can be found using the relationship <code class='latex inline'>\sin \theta = \frac{d}{BC}</code>.</p> <p>In a parallelogram, two adjacent sides measure <code class='latex inline'>10 cm</code> and <code class='latex inline'>12 cm</code>. The shorter diagonal is <code class='latex inline'>15 cm</code>. Determine, to the nearest degree, the measures of all four angles in the parallelogram.</p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 34^{\circ}</code></p> <p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22860" /> <p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6770" /> <p>Calculate <code class='latex inline'>\sin T</code> in each triangle. Then, find <code class='latex inline'>\angle T</code>, to the nearest degree.</p><img src="/qimages/6753" /> <p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22880" /> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65221" /> <p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the cosine ratio.</p><img src="/qimages/22868" /> <p>Draw two parallelograms that are similar.</p> <p>The mainsail of the small sailboat shown below measures <code class='latex inline'>\displaystyle 2.4 \mathrm{~m} </code> across the boom and <code class='latex inline'>\displaystyle 4.4 \mathrm{~m} </code> up the mainmast. The boom and mast meet at an angle of <code class='latex inline'>\displaystyle 74^{\circ} </code>. What is the area of the mainsail to the nearest tenth of a square metre?</p><img src="/qimages/165166" /><p>uooq</p><p>ұseuu!̣eu</p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin M = \dfrac{3}{4}</code></p> <p>Name the two similar triangles and explain why they are similar.</p><img src="/qimages/22876" /> <p>Solve each of the following triangles. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.</p><img src="/qimages/22874" /> <p>Find the measure of both acute angles in the triangle, to the nearest degree.</p><img src="/qimages/9461" /> <p> Find the value of <code class='latex inline'>\sin \theta</code> and <code class='latex inline'>\cos \theta</code> if <code class='latex inline'>\tan \theta = \frac{5}{7}</code>. Leave your answer in exact value.</p> <p>Cory is building a ramp for his school theatre production. It must climb a height of <code class='latex inline'>60</code> cm and have a slope angle of 10°.</p><p>a) Draw a diagram and label the given information.</p><p>b) What distance will the ramp run along the floor?</p><p>c) What will the distance along the surface of the ramp be?</p> <p>Find the measure of each angle, to the nearest degree.</p><p>tan D = <code class='latex inline'>\dfrac{13}{7}</code></p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin \theta = 0.7824</code></p> <p>Martin is installing an array of solar panels 3.8 m high in his backyard. The array needs to be tilted <code class='latex inline'>60^o</code> from the ground. Municipal bylaws restrict residents from having any secondary structures taller than 3.0 m. Will Martin be able to build his array? Include calculations in your explanation.</p> <p> One of Canada&#39;s tallest trees is a Douglas fir on Vancouver Island. The angle of elevation measured by an observer who is <code class='latex inline'> 78 \mathrm{~m} </code> from the base of the tree is <code class='latex inline'> 50^{\circ} </code> . How tall is this tree, to the nearest metre?</p><img src="/qimages/65235" /> <p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65392" /> <p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>28.3^{\circ}</code></p> <p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6766" /> <p>Find the measure of <code class='latex inline'>\angle A</code>, to the nearest degree.</p><img src="/qimages/5470" /> <p>A radio transmitter is to be supported with a guy wire. The wire is to form a 65° angle with the ground and reach 30 m up the transmitter. The wire can be ordered in whole-number lengths of metres. How much wire should be ordered?</p><img src="/qimages/6774" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin F = 0.8156</code></p> <p>Find <code class='latex inline'> \angle W </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan W=\frac{15}{9} </code></p> <p>Find <code class='latex inline'> \angle Q </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos Q=\frac{5}{11} </code></p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 90^{\circ}</code></p> <p>Decide whether each statement is true or false. Justify your decision.</p><p><code class='latex inline'>\cos \theta \doteq 0.8929</code></p><img src="/qimages/1023" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth.</p><img src="/qimages/22852" /> <p>For each triangle, calculate <code class='latex inline'>x</code> to the nearest centimetre.</p><img src="/qimages/2279" /> <p>Determine whether these triangles are similar. If they are similar, write a proportion statement and determine the scale factor.</p><img src="/qimages/7279" /> <p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22859" /> <p>Draw two hexagons that are similar.</p> <p>Find <code class='latex inline'> \angle W </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan W=\frac{7}{4} </code></p> <p>Calculate <code class='latex inline'> \cos \mathrm{T} </code> in each triangle. Then, find <code class='latex inline'> \angle \mathrm{T} </code> , to the nearest degree.</p><img src="/qimages/65379" /> <p>Find the perimeter and area of each triangle. Round to the nearest hundredth.</p><img src="/qimages/104254" /> <p>When a ladder is rested against a tree, the foot of the ladder is <code class='latex inline'> 1 \mathrm{~m} </code> from the base of the tree and forms an angle of <code class='latex inline'> 64^{\circ} </code> with the ground. How far up the tree does the ladder reach, to the nearest tenth of a metre?</p><img src="/qimages/65233" /> <p>The world’s longest escalator is in the subway system in St. Petersburg, Russia. The escalator is <code class='latex inline'>330.7</code> m long and rises a vertical distance of <code class='latex inline'>59.7</code> m. What 1is the angle of elevation of the top of the escalator when viewed from the bottom, to the nearest degree?</p> <p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104238" /> <p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>. Round to the nearest tenth.</p><img src="/qimages/104262" /> <p>ROLLER COASTERS The angle of ascent of the first hill of a roller coaster is <code class='latex inline'>\displaystyle 55^{\circ} </code>. If the length of the track from the beginning of the ascent to the highest point is 98 feet, what is the height of the roller coaster when it reaches the top of the first hill?</p><img src="/qimages/104233" /> <p>Solve <code class='latex inline'>\triangle FGH</code>.</p><img src="/qimages/5484" /> <p>Find each trigonometric ratio for angle <code class='latex inline'>A</code> in the triangle at the right. </p><img src="/qimages/60797" /><p><code class='latex inline'>\displaystyle \tan A </code></p> <p>In <code class='latex inline'>\triangle DEF </code>, </p><p><code class='latex inline'>DF = 6.0 km</code>, <code class='latex inline'>\angle E = 44^o, \angle F = 90^o</code></p><p>a) Draw this triangle and label the given information.</p><p>b) Solve <code class='latex inline'>\triangle DEF</code>.</p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin U = \dfrac{5}{11}</code></p> <p>A surveyor has mapped out a property as shown at the left. Determine the length of sides <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code> to the nearest metre.</p><img src="/qimages/165757" /> <p>John&#39;s garden is in the shape of a right isosceles triangle with base <code class='latex inline'>3.4</code> m. If she enlarges her garden to a similar shape whose base is doubled, what will the area of her new garden be?</p><img src="/qimages/5469" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2387" /> <p>Theresa and Branko are competing in a series of outdoor challenges that will eventually lead them to a hidden treasure. Each clue they find helps them find a new clue. Theresa is getting ready to climb a steep cliff to find their next clue at the Lookout Point. She has two options:</p> <ul> <li>Option A: Climb straight up the cliff, and then jog over to Lookout Point.</li> <li>Option B: Climb directly to Lookout Point along the diagonal shown.</li> </ul> <img src="/qimages/9399" /><p>She is awaiting instructions from Branko, who is positioned directly facing Lookout Point at a distance of 30 m from the base of the cliff.</p><p>From Branko’s point of View, Lookout Point is at an angle of elevation of 68°. He also observes that the diagonal path up the cliff makes a 73° angle with the ground. Branko knows that Theresa can climb at a speed of 1.0 m/s and jog at a speed of 5.0 m/s after a climb. It is a tight race and seconds count. Which option should Branko tell Theresa to take: A or B?</p> <p>Find the measure of <code class='latex inline'>\angle B</code>, to the nearest degree.</p><img src="/qimages/22885" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan V = \dfrac{17}{9}</code></p> <p> Find <code class='latex inline'> \sin \mathrm{A} </code> and <code class='latex inline'> \sin \mathrm{C} </code> in each triangle. Round answers to the nearest thousandth, if necessary.</p><img src="/qimages/65258" /> <p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p><code class='latex inline'>\tan 22.5^{\circ}</code></p> <p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{2}{3} </code></p> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2382" /> <p>In <code class='latex inline'>\triangle PQR</code>, <code class='latex inline'>\angle R = 90^o</code> and <code class='latex inline'>p = 12.0 cm</code>.</p><p>a) Determine <code class='latex inline'>r</code>, when <code class='latex inline'>\angle Q = 53^o</code></p><p>b) Determine <code class='latex inline'>\angle P</code>, when <code class='latex inline'>q = 16.5 cm</code>.</p> <p>What are the following values?</p> <ul> <li><code class='latex inline'>\tan 0^o</code></li> <li><code class='latex inline'>\tan 45^o</code></li> <li><code class='latex inline'>\tan 90^o</code></li> </ul> <p>Show your work.</p> <p>No positive number is an integer.</p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos C = 0.7824</code></p> <p>A spotlight on a 3.0 m Stand shines on the surface of a swimming pool. The beam of light hits the water at a point 7.0 m away from the base of the stand.</p><img src="/qimages/5296" /><p>a) Calculate the angle the beam makes with the pool surface. Round your answer to the nearest degree.</p><p>b) The beam reflects off the pool surface and strikes a wall 4.5 m away from the reflection point. The angle the beam makes with the pool is exactly the same on either side ofrhe reflection point. Calculate how far up the wall, to the nearest tenth of a metre, the spotlight will appear.</p> <p>A scuba diver swam north at 1.5 m/s. across a current running from east to west at 2.0 m/s. She swam for 3 min and then surfaced.</p><p>a) Draw a diagram showing where the dive boat will pick her up relative to where she dove.</p><p>b) How far did she travel?</p> <p> Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\displaystyle \begin{array}{llll} &a) & \cos 80.2^o &b) & \cos 45^o\\ &c) & \cos 30^o &d) & \cos 60^o\\ &e) & \cos 89^o &f) & \cos 0^o\\ &g) & \cos 5^o &h) & \cos 83^o \end{array} </code></p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 29^{\circ}</code></p> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65311" /> <p> Triangle ABC has a base BC = 115 cm, side BA = 80 cm, and <code class='latex inline'>\angle B = 35^{\circ}</code>. Determine the height h from the vertex A and the area of <code class='latex inline'>\triangle ABC.</code> Leave your answer in exact value.</p> <p> Determine the measurements of the indicated angles and sides.</p><img src="/qimages/1609" /> <p>A flagpole casts a shadow <code class='latex inline'>28</code> m long when the Sun’s rays make an angle of <code class='latex inline'>25^o</code> with the ground. How tall is the flagpole, to the nearest metre?</p> <p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22856" /> <p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104240" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan X = \dfrac{3}{5}</code></p> <p>Solve each triangle.</p><img src="/qimages/6761" /> <p>Find the missing values: <strong>a</strong> and <strong>b</strong>. Leave your answer in exact value.</p><img src="/qimages/248" /> <p>Find the length of <code class='latex inline'>x</code>. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6764" /> <p> Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65411" /> <p>Find <code class='latex inline'>\displaystyle \angle \mathrm{B} </code>, to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan B=3.025 </code></p> <p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/22866" /> <p>Find <code class='latex inline'>x</code>, to the nearest tenth of a centimetre.</p><img src="/qimages/5472" /> <p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>.</p><img src="/qimages/104285" /> <p>Decide whether each statement is true or false. Justify your decision.</p><p><code class='latex inline'>\tan \alpha = 2</code></p><img src="/qimages/1023" /> <p>Find the measure of <code class='latex inline'>\angle A</code>, to the nearest degree.</p><img src="/qimages/9424" /> <p>Giulia unreels her kite string until the kite is flying on a string of length 50m. </p><p>A light breeze holds the kite such that the sting make and angle of <code class='latex inline'>60^o</code> with the ground. After a few minutes, the wind pickup speed. The wind now pushes the kite until the string makes an angle of <code class='latex inline'>45^o</code> with the ground. </p><p>What distance has the kite changed position horizontally over the ground. Determine an exact expression. </p> <p>Does <code class='latex inline'>\cos60^{\circ}=\displaystyle{\frac{1}{2}}</code> mean that the side adjacent to the <code class='latex inline'>60^{\circ}</code> angle measure 1 unit and the hypotenuse measure 2 units? Explain.</p> <p>A <code class='latex inline'>\displaystyle 3 \mathrm{~m} </code> ladder can be used safely only at an angle of <code class='latex inline'>\displaystyle 75^{\circ} </code> with the horizontal. How high, to the nearest metre, can the ladder reach?</p> <p>Mannpreet is standing 8.1 m from a flagpole. His eyes are 1.7 m above ground. The top of the flagpole has an angle of elevation of35°. How tall, to the nearest tenth of a metre, is the flagpole?</p> <p>Determine <code class='latex inline'>x</code> to the nearest unit and angle <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/5307" /> <p>To photograph a rocket stage separating, Lucien mounts his camera on a tripod. The tripod can be set to the angle at which the stage will separate. This is where Lucien needs to aim his lens. He begins by aiming his camera at the launch pad, which is 1500 m away. The stage will separate at 20 000 m. At what angle should Lucien set the tripod?</p> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6960" /> <p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the cosine ratio.</p><img src="/qimages/22867" /> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 5^{\circ} </code></p> <p>A coaSt guard boat is tracking two ships using radar. At noon, the ships are 5.0 km apart and the angle between them is 90°. The closest ship is 3.1 km from the coast guard boat. How far, to the nearest tenth of a kilometre, is the Other ship from the coast guard boat?</p><img src="/qimages/5297" /> <p>Solve each triangle.</p><img src="/qimages/6763" /> <p>Find the length of x, to the nearest tenth of a unit.</p><img src="/qimages/9466" /> <p>The Great Pyramid of Cheops is a square-based pyramid with a height of 147 m and a base length of 230 m. Find the angle, <code class='latex inline'>\theta</code>, to the nearest degree, that one of the edges of the pyramid makes with the base.</p><img src="/qimages/5492" /> <p>Determine <code class='latex inline'>y'</code>.</p><p><code class='latex inline'>y=x^2\sin x</code></p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos \theta = \dfrac{3}{10}</code></p> <p>Find the measures of both acute angles in each triangle, to the nearest degree. </p><img src="/qimages/2377" /> <p>An overhead Streetlight can illuminate a circular area of diameter 14 m. The light bulb is 6.8 m directly above a bike path. Determine the angle of elevation, to the nearest degree, from the edge of the illuminated area to the light bulb.</p><img src="/qimages/5298" /> <p>Each side length of regular pentagon <code class='latex inline'>ABCDE</code> is 8.2 cm.</p><p>Calculate the measure of <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/1054" /> <p>The sides of an isosceles triangle are 12 cm. 12 cm, and 16 cm. Use primary trigonometric ratios to determine the largest interior angle to the nearest degree. (Hint: Divide the triangle into two congruent right triangles.)</p> <p>Solve this triangle.</p><img src="/qimages/9928" /> <p>Determine the angle between the line <code class='latex inline'>y=\displaystyle{\frac{3}{2}}x+4</code> and the x-axis.</p> <p>Draw two kites that are congruent.</p> <p>For a ladder to be stable, the angle that it makes with the ground should be no more than 78<code class='latex inline'>^{\circ}</code> and no less than 73<code class='latex inline'>^{\circ}</code>.</p> <ul> <li>If the base of a ladder that is 8.0 m long is placed 1.5 m from a wall, what is the angle between the ground and the ladder? Is this safe?</li> </ul> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos R = 0.5683</code></p> <p>During take-off a plane must rise at least 20m during its first 1.5 km of flight to successfully clear the runway.</p><img src="/qimages/6759" /><p>a) At what minimum average angle must the plane climb for a safe take-off, to the nearest hundredth of a degree?</p><p>b) If the required rise is doubled to 40 m, does this double the climb angle? Explain.</p> <p>Find the measures of both acute angles in each triangle to the nearest degree.</p><img src="/qimages/22847" /> <p>For a ladder to be stable, the angle that it makes with the ground should be no more than 78<code class='latex inline'>^{\circ}</code> and no less than 73<code class='latex inline'>^{\circ}</code>.</p><p> What are the minimum and maximum safe distances from the base of the ladder to the wall?</p> <p>An octahedron is formed by attaching eight congruent equilateral triangles, as shown.</p><img src="/qimages/5489" /><p>If the length along one of the edges is 20 cm, find the distance between opposite vertices.</p> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6963" /> <p>Find the measure of both acute angles in the triangle, to the nearest degree.</p><img src="/qimages/9459" /> <p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.712 </code></p> <p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos P=0.019 </code></p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos P = \dfrac{1}{7}</code></p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos \theta = 0.5143</code></p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 50^{\circ}</code></p> <p>Find each trigonometric ratio for angle <code class='latex inline'>A</code> in the triangle at the right. </p><img src="/qimages/60797" /><p><code class='latex inline'>\displaystyle \cos A </code></p> <p>Find the length of x, to the nearest tenth of a metre, then the measure of y, to the nearest degree.</p><img src="/qimages/6777" /> <p>GYMNASTICS The springboard that Eric uses in his gymnastics class has 6-inch coils and forms an angle of <code class='latex inline'>\displaystyle 14.5^{\circ} </code> with the base. About how long is the springboard?</p><img src="/qimages/104231" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin \theta = \dfrac{4}{9}</code></p> <p> A group of students measured a distance of 50 cm from the base of a pole CB to a point A. If <code class='latex inline'>\angle CAB = 16.5^{\circ}</code>, calculate the height of the pole, correct to one decimal. Leave your answer in exact value.</p><img src="/qimages/247" /> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65314" /> <p>After <code class='latex inline'>1 h</code>, an airplane has travelled 350 km. Strong winds, however, have caused the plane to be 48 km west of its planned flight path. By how many degrees is the airplane off its planned flight path?</p><img src="/qimages/1050" /> <p>State all the primary trigonometric ratios for <code class='latex inline'>\angle A</code> and <code class='latex inline'>\angle C</code>. Then determine <code class='latex inline'>\angle A</code> and <code class='latex inline'>\angle D</code> to the nearest degree.</p><img src="/qimages/2277" /> <p>Calculate <code class='latex inline'> \cos \mathrm{A} </code> and <code class='latex inline'> \cos \mathrm{C} </code> in each triangle. Round answers to the nearest thousandth, if necessary.</p><img src="/qimages/65336" /> <p> The hypotenuse of a right triangle is <code class='latex inline'> 10 \mathrm{~cm} </code> long. How long is the side adjacent to the <code class='latex inline'> 21^{\circ} </code> angle, to the nearest tenth of a centimetre?</p> <img src="/qimages/10074" /><p>What is the value of <code class='latex inline'>\displaystyle \theta </code> to the nearest degree?</p><p>A. <code class='latex inline'>\displaystyle 25^{\circ} </code></p><p>C. <code class='latex inline'>\displaystyle 23^{\circ} </code></p><p>B. <code class='latex inline'>\displaystyle 65^{\circ} </code></p><p>D. <code class='latex inline'>\displaystyle 67^{\circ} </code></p> <p>Find <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/22888" /> <p><code class='latex inline'>\triangle</code> ABC is an isosceles triangle. The height of the triangle is 3 cm, and the two acute angles at its base are each 56°. How long are the two equal sides, to the nearest tenth of a centlmetre?</p><img src="/qimages/6758" /> <p>An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55<code class='latex inline'>^{\circ}</code>. Determine the area of the triangle.</p> <img src="/qimages/104266" /><p>Ch. MULTIPLE REPRESENTATIONS In this problem, you will investigate an algebraic relationship between the sine and cosine ratios.</p><p>a. Geometric Draw three right triangles that are not similar to each other. Label the triangles <code class='latex inline'>\displaystyle A B C, M N P </code>, and <code class='latex inline'>\displaystyle X Y Z </code>, with the right angles located at vertices <code class='latex inline'>\displaystyle B, N </code>, and <code class='latex inline'>\displaystyle Y </code>, respectively. Measure and label each side of the three triangles.</p><p>b. Tabular Copy and complete the table below.</p><img src="/qimages/104267" /><p>Triangle &amp; \multicolumn{3}{|c|} { Trigonometric Ratios } &amp; \multicolumn{2}{|c|} { Sum of Ratios Squared } \multirow{2}{<em>} {<code class='latex inline'>\displaystyle A B C </code>} &amp; <code class='latex inline'>\displaystyle \cos A </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin A </code> &amp; <code class='latex inline'>\displaystyle (\cos A)^{2}+(\sin A)^{2}= </code> &amp; \cline { 2 - 7 } &amp; <code class='latex inline'>\displaystyle \cos C </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin C </code> &amp; &amp; <code class='latex inline'>\displaystyle (\cos C)^{2}+(\sin C)^{2}= </code> &amp; \multirow{2}{</em>} { MNP } &amp; <code class='latex inline'>\displaystyle \cos M </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin M </code> &amp; <code class='latex inline'>\displaystyle (\cos M)^{2}+(\sin M)^{2}= </code> &amp; \cline { 2 - 6 } &amp; <code class='latex inline'>\displaystyle \cos P </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin P </code> &amp; <code class='latex inline'>\displaystyle (\cos P)^{2}+(\sin P)^{2}= </code> &amp; \multirow{2}{*} {<code class='latex inline'>\displaystyle X Y Z </code>} &amp; <code class='latex inline'>\displaystyle \cos X </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin X </code> &amp; <code class='latex inline'>\displaystyle (\cos X)^{2}+(\sin X)^{2}= </code> &amp; \cline { 2 - 6 } &amp; <code class='latex inline'>\displaystyle \cos Z </code> &amp; &amp; <code class='latex inline'>\displaystyle \sin Z </code> &amp; <code class='latex inline'>\displaystyle (\cos Z)^{2}+(\sin Z)^{2}= </code> &amp;</p><img src="/qimages/104268" /><p>C. Verbal Make a conjecture about the sum of the squares of the cosine and sine of an acute angle of a right triangle.</p><p>d. Algebraic Express your conjecture algebraically for an angle <code class='latex inline'>\displaystyle X </code>.</p><p>e. Analytical Show that your conjecture is valid for angle <code class='latex inline'>\displaystyle A </code> in the figure at the right using the trigonometric functions and the Pythagorean Theorem.</p> <p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6769" /> <p>Determine the value of <code class='latex inline'>\theta</code>, to the nearest degree, in each triangle.</p><img src="/qimages/1032" /> <p>The angle of elevation of the top of a sail on a sailboat is <code class='latex inline'>72^{\circ}</code>. The horizontal length of the sail is 0.8 m. What is the vertical height of the sail, to the nearest tenth of a metre?</p> <p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos P=0.524 </code></p> <p>Solve the triangle. Round lengths to the nearest unit and angle measures to the nearest degree.</p><img src="/qimages/9429" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin K = \dfrac{7}{23}</code></p> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 60^{\circ} </code></p> <p>Find all the angles in <code class='latex inline'>\angle WXY</code>, to the nearest degree.</p><img src="/qimages/6773" /> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 25^{\circ} </code></p> <p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104225" /> <p>Find the measure of both acute angles in each triangle, to the nearest degree.</p><img src="/qimages/5475" /> <p>The hypotenuse of a right triangle is 10 m long. How long is the side adjacent to the 21° angle, to the nearest tenth of a metre?</p> <p>Find the measures of both acute angles in each triangle, to the nearest degree. </p><img src="/qimages/2379" /> <p>In <code class='latex inline'>\triangle PQR</code>, <code class='latex inline'>\angle Q = 90^o</code> and <code class='latex inline'>PR = 20 cm</code>. Find <code class='latex inline'>PQ</code>, to the nearest tenth of centimeter, if <code class='latex inline'>\angle R = 41^o</code>.</p> <p>Find the cosine of the smaller acute angle in a triangle with side lengths of 10,24 , and 26 inches.</p> <p>Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/9476" /> <p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. </p><p><code class='latex inline'>\displaystyle 3.2,5.3,8.6 </code></p> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin D = \dfrac{14}{19}</code></p> <p>Find the measure of both acute angles in each triangle, to the nearest degree.</p><img src="/qimages/5479" /> <p>Find <code class='latex inline'> \angle Q </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos \mathrm{Q}=\frac{3}{14} </code></p> <p>Solve each triangle. Round each length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/165163" /> <p>Darrel wants to lean planks of wood that are 1.5 m, 1.8 m, and 2.1 m long against the wall inside hi garage. If the top of a plank forms an angle of less than <code class='latex inline'>10^o</code> with the wall, the plank might fall over. If the bottom of a plank sticks out more than 30 cm from the wall, Darrel won&#39;t have rom to park his car. Will Darrel be able to store all three planks in the garage? Justify your solution.</p><img src="/qimages/2291" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos S = \dfrac{3}{7}</code></p> <ol> <li>Calculate tan <code class='latex inline'>\displaystyle D, \angle D, \tan E </code>, and <code class='latex inline'>\displaystyle \angle E </code>. Round each angle measure to the nearest degree.</li> </ol> <img src="/qimages/65212" /> <p>Find the measure of each angle to the nearest tenth of a degree using the Distance Formula and an inverse trigonometric ratio. <code class='latex inline'>\displaystyle \angle K </code> in right triangle <code class='latex inline'>\displaystyle J K L </code> with vertices <code class='latex inline'>\displaystyle J(-2,-3), K(-7,-3) </code>, and <code class='latex inline'>\displaystyle L(-2,4) </code></p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 43^{\circ}</code></p> <p>Salma is at the top of a cliff looking down at Rico’s boat. They both have Global Positioning System (CPS) devices and are communicating via cell phones. They determine that Rico’s boat is 5.0 km from a point on the shore directly below Salma, and 6.0 km from Salma herself.</p><p>a) Draw a diagram to represent this situation and label the given information.</p><p>b) Find the angle of depression at which Salma is viewing Rico’s boat.</p><p>c) Find the height of the cliff.</p> <p>When it is leaning against a wall, the foot of a ladder is 2 In from the base of the wall. The angle between the ladder and the ground is 75°.</p><p>a) How high up the wall does the ladder reach, to the nearest centimetre?</p><img src="/qimages/6775" /><p>b) How long is the ladder, to the nearest centimetre?</p><p>c) If the ladder slips down the wall so that it makes an angle of 55° with the ground, does the end on the ground slip more than the end against the wall? Explain.</p> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 65^{\circ}</code></p> <p>Determine all unknown sides to the nearest unit and all unknown interior angles to the nearest degree.</p><img src="/qimages/2284" /> <p>Find the perimeter and area of each triangle. Round to the nearest hundredth.</p><img src="/qimages/104255" /> <p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22845" /> <ol> <li>In <code class='latex inline'>\displaystyle \triangle \mathrm{DEF} </code>, find <code class='latex inline'>\displaystyle \angle \mathrm{F} </code>, to the nearest degree, if <code class='latex inline'>\displaystyle \mathrm{DE}=15 \mathrm{~cm}, \mathrm{DF}=18 \mathrm{~cm} </code>, and <code class='latex inline'>\displaystyle \angle \mathrm{E}=90^{\circ} </code>.</li> </ol> <p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22881" /> <p>In <code class='latex inline'>\triangle XYZ </code>, </p><p><code class='latex inline'>XY = 16 cm, YZ = 11 cm, \angle Z = 90^o</code></p><p>a) Draw this triangle and label the given information.</p><p>b) Solve <code class='latex inline'>\triangle XYZ</code>.</p> <p>A guy wire is attached to a cellphone tower as shown at the left. The guy wire is 30 m long, and the cellphone tower is 24 m high. Determine the angle that is formed by the guy wire and the ground.</p><img src="/qimages/1049" /> <p>Leah and Auggie are hiking in a park. The location of the entrance to the park information centre, and picnic area are shown.</p><img src="/qimages/22855" /><p>a) At what angle to the line connecting the park entrance and the information centre should Leah and Auggie hike to reach the picnic area in the shortest distance? Round to the nearest degree.</p><p>b) Describe any assumptions you make in your solution.</p> <p>The side adjacent to the 74° angle in a right triangle is 6 cm long. How long is the hypotenuse, to the nearest tenth of a centimetre?</p> <p>a) Determine the three primary trigonometric ratios for <code class='latex inline'>\angle A</code>.</p><img src="/qimages/9926" /><p>b) Calculate the measure of <code class='latex inline'>\angle A</code> to the nearest degree.</p> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2384" /> <p>If <code class='latex inline'>\tan \theta = \frac{4}{5}</code>, which one of of the following statements must be true?</p><p><strong>(a)</strong> Hypotenuse is double the length of Adjacent </p><p><strong>(b)</strong> Opposite is longer than Adjacent </p><p><strong>(c)</strong> Opposite is shorter than Adjacent </p><p><strong>(d)</strong> Opposite is triple the length of Adjacent </p><p><strong>(e)</strong> Hypotenuse is longer than the sum of Adjacent and Opposite </p> <p>Find x, to the nearest tenth of a unit.</p><img src="/qimages/9426" /> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 89^{\circ} </code></p> <p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>83^{\circ}</code></p> <p>Find the length of x, to the nearest tenth of a unit.</p><img src="/qimages/9467" /> <p>Solve for <code class='latex inline'>x</code>, and express your answer to one decimal place.</p><p> <code class='latex inline'>\sin62^{\circ}=\displaystyle{\frac{x}{14}}</code></p> <p>From a spot <code class='latex inline'>\displaystyle 25 \mathrm{~m} </code> from the base of the Peace Tower in Ottawa, the angle of elevation to the top of the flagpole is <code class='latex inline'>\displaystyle 76^{\circ} </code>. How tall, to the nearest metre, is the Peace Tower, including the flagpole?</p> <p>The observation deck at Justin&#39;s Cove lighthouse, in Prince Edward Island is about <code class='latex inline'>20</code> m above sea level. From the observation deck. the angle of depression of a boat on the water is <code class='latex inline'>6</code>°. How far is the boat from the lighthouse, to the nearest metre?</p> <p>The Capilano Suspension Bridge in North Vancouver is the world’s highest footbridge of its kind. The bridge is 140 m long. From the ends of the bridge, the angles of depression of a point on the river under the bridge are 41° and 48°. How high is the bridge above the river, to the nearest metre?</p> <p>A 200 m cable attached to the top of an antenna makes an angle of <code class='latex inline'>37^o</code> with the ground. How tall is the antenna to the neares</p> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \tan 30^{\circ} </code></p> <p>Determine the value of <code class='latex inline'>\theta</code>, to the nearest degree, in each triangle.</p><p> <img src="/qimages/1033" /></p> <p>Find the measure of each angle to the nearest tenth of a degree using the Distance Formula and an inverse trigonometric ratio. <code class='latex inline'>\displaystyle \angle Y </code> in right triangle <code class='latex inline'>\displaystyle X Y Z </code> with vertices <code class='latex inline'>\displaystyle X(4,1), Y(-6,3) </code>, and <code class='latex inline'>\displaystyle Z(-2,7) </code></p> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 45^{\circ} </code></p> <p>A tree branch 3 m above ground runs parallel to Noel’s garage and his neighbours. Noel wants to attach a rope swing on this branch. The garages are 4.2 m apart and the rope is 2.7 m long.</p><img src="/qimages/2294" /><p>a) What is the maximum angle, measured from the perpendicular, through which the rope can swing? Round your answer to the nearest degree.</p><p>b) What is the maximum height above ground, to the nearest tenth of a metre, of the end of the rope?</p> <p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/22863" /> <p>Find the measure of both acute angles in each triangle, to the nearest degree.</p><img src="/qimages/5476" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth.</p><img src="/qimages/22853" /> <p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 54^{\circ}</code></p> <p>ABCD is a rectangle with AB = 15 cm and BC = 10 cm. What is the measure of <code class='latex inline'>\angle BAC</code> to the nearest degree?</p><img src="/qimages/9927" /> <p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 0^{\circ} </code></p> <p>The pitch of a roof is the rise divided by the run. If the pitch is greater than 1.0 but less than 1.6, roofers use planks fastened to the roof to stand on when shingling it. If the pitch is greater than 1.6, scaffolding is needed. For each roof angle, what equipment (scaffolding or planks), if any, would roofers need?</p><p>a) <code class='latex inline'>\theta = 34^o</code></p><p>b) <code class='latex inline'>\theta = 60^o</code></p><p>c) <code class='latex inline'>\theta = 51^o</code></p> <p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. <code class='latex inline'>\displaystyle 11,12,24 </code></p> <p>A bridge is going to be built across a river. To determine the width of the river, a surveyor on one bank sights the top of a pole, which is 3 m high, on the opposite bank. His optical device is mounted 1.2 m above the ground. The angle of elevation to the top of the pole is 85<code class='latex inline'>^{\circ}</code>. How wide is the river?</p> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65225" /> <p>Determine the length of the indicated side or the measure of the indicated angle.</p><img src="/qimages/6192" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos Z = 0.4923</code></p> <p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the cosine ratio.</p><img src="/qimages/22869" /> <p> Calculate <code class='latex inline'> \cos \mathrm{A} </code> and <code class='latex inline'> \cos \mathrm{C} </code> in each triangle. Round answers to the nearest thousandth, if necessary.</p><img src="/qimages/65335" /> <p>Find the length of x, to the nearest tenth of a unit.</p><img src="/qimages/9465" /> <p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104226" /> <p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65229" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan K = 1.3175</code></p> <p>From the top of the CN Tower, the angle of depression to the tip of the tower’s shadow is 88°. The shadow is 19.5 m long. How tall is the CN Tower?</p> <p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>60^{\circ}</code></p> <p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104237" /> <p>The world’s longest covered bridge crosses the Saint John River in Hartland, New Brunswick. From two points, <code class='latex inline'>X</code> and <code class='latex inline'>Y</code>, 100 m apart on the same side of the river, the lines of sight to the far end of the bridge, <code class='latex inline'>Z</code>, make angles of 85.6° and 79.8° with the river bank, as shown. What is the length of the bridge, <code class='latex inline'>b</code>, to the nearest <code class='latex inline'>10</code> m?</p><img src="/qimages/5486" /> <p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos N = 0.2197</code></p> <p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22857" /> <p>Determine <code class='latex inline'>x</code> to the nearest unit and angle <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/5306" /> <p> In <code class='latex inline'> \triangle \mathrm{ABC}, a=32 \mathrm{~cm}, b=35 \mathrm{~cm} </code> , and <code class='latex inline'> c=29 \mathrm{~cm} </code> . Find the measure of the largest angle, to the nearest degree.</p> <p>Mia walked diagonally across a rectangular field measuring 58 m by 74 m. To the nearest degree, at what angle with respect to the shorter side did she walk?</p> <p>Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.</p><img src="/qimages/104245" /> <p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>. Round to the nearest tenth.</p><img src="/qimages/104261" /> <p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104235" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6964" /> <p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65391" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2386" /> <p>Determine the indicated side lengths in the triangles.</p><img src="/qimages/6191" /> <p>Calculate <code class='latex inline'>\cos T</code> in each triangle. Then, find <code class='latex inline'>\angle T</code>, to the nearest degree.</p><img src="/qimages/6755" /> <p>Toby uses chains and a winch to lift engines at his father&#39;s garage. Two hooks in the ceiling are <code class='latex inline'>\displaystyle 2.8 \mathrm{~m} </code> apart. Each hook has a chain hanging from it. The chains are of length <code class='latex inline'>\displaystyle 1.9 \mathrm{~m} </code> and <code class='latex inline'>\displaystyle 2.2 \mathrm{~m} </code>. When the ends of the chains are attached, they form an angle of <code class='latex inline'>\displaystyle 86^{\circ} </code>. In this configuration, what acute angle, to the nearest degree, does each chain make with the ceiling?</p><img src="/qimages/165734" /> <p>Solve each triangle. Round each length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/165162" /> <p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6765" /> <p> Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65430" /> <p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6957" /> <p>SCHOOL SPIRIT Hana is making a pennant for each of the 18 girls on her basketball team. She will use <code class='latex inline'>\displaystyle \frac{1}{2} </code> -inch seam binding to finish the edges of the pennants.</p><p>a. What is the total length of seam binding needed to finish all of the pennants?</p><p>b. If seam binding is sold in 3-yard packages at a cost of <code class='latex inline'>\displaystyle \$ 1.79 </code>, how much will it cost?</p><img src="/qimages/104252" />
<p>A cat, sitting in the top of a tree, spots a dog and a firefighter, both on the flat ground below. From the cat’s point of view, the dog is 10 m south, at an angle of depression of 65°, and the firefighter is some distance east of the tree, at an angle of depression of 50°. How far is the firefighter from the dog?</p>
<p>Find <code class='latex inline'>\displaystyle \angle \mathrm{B} </code>, to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan B=0.600 </code></p>
<p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>.</p><img src="/qimages/104286" />
<p>The diagram shows a roofing truss with <code class='latex inline'>\displaystyle A B </code> parallel to <code class='latex inline'>\displaystyle C D </code>. Calculate the total length of wood needed to construct the truss. Round your answer to the nearest metre.</p><img src="/qimages/165748" />
<p>Solve each triangle.</p><img src="/qimages/6760" />
<p>Calculate the measure of <code class='latex inline'>x</code> in the diagram to the nearest degree, using one of the primary trigonometric ratios.</p><img src="/qimages/1024" />
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 0^{\circ} </code></p>
<p>Identify the primary trigonometric ratio for <code class='latex inline'>\theta</code> that is equal to each ratio for the triangle.</p><p><strong>a)</strong> <code class='latex inline'>\displaystyle{\frac{50}{54}}</code></p><p><strong>b)</strong> <code class='latex inline'>\displaystyle{\frac{20}{50}}</code></p><p><strong>c)</strong> <code class='latex inline'>\displaystyle{\frac{20}{54}}</code></p><img src="/qimages/1025" />
<p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos P=0.343 </code></p>
<p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65383" />
<p>An underground parking lot is being constructed 8.00 m below ground level.</p><p>a) If the exit ramp is to rise at an angle of <code class='latex inline'>15^o</code>, how long will the ramp be? Round your answer to the nearest hundredth of a metre.</p><p>b) What horizontal distance, to the nearest hundredth of a metre, 1.5 needed for the ramp?</p>
<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/22849" />
<p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104228" />
<p>A wooden boat is 4 km west of a buoy, A canoe is 5 km south of the buoy_</p><p>a) How far, to the nearest tenth of a kilometre, is the wooden boat from the canoe?</p><p>b) At what angle south of due east, to the nearest degree, should the wooden boat travel to reach the canoe?</p>
<p>Find the three primary trigonometric ratios for <code class='latex inline'>\angle A</code>, to four decimal places.</p><img src="/qimages/6752" />
<img src="/qimages/10073" /><p>Which statement about <code class='latex inline'>\displaystyle \triangle A B C </code> is true?</p><p>A. <code class='latex inline'>\displaystyle \sin B=\frac{a}{c} </code></p><p>B. <code class='latex inline'>\displaystyle \cos A=\frac{a}{c} </code></p><p>C. <code class='latex inline'>\displaystyle \tan B=\frac{a}{b} </code></p><p>D. <code class='latex inline'>\displaystyle \sin A=\cos B </code></p>
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65220" />
<p>Find the length of x. to the nearest tenth of a unit. by applying the cosine ratio.</p><img src="/qimages/6771" />
<ol> <li>In <code class='latex inline'>\displaystyle \triangle \mathrm{PQR}, \angle \mathrm{Q}=90^{\circ} </code>, and <code class='latex inline'>\displaystyle \mathrm{PR}=20 \mathrm{~cm} . </code> Find <code class='latex inline'>\displaystyle \mathrm{PQ} </code>, to the nearest tenth of a centimetre, if <code class='latex inline'>\displaystyle \angle \mathrm{R}=41^{\circ} . </code></li> </ol>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan B = 0.7425</code></p>
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6750" />
<p>Calculate <code class='latex inline'>\cos T</code> in each triangle. Then, find <code class='latex inline'>\angle T</code>, to the nearest degree.</p><img src="/qimages/6756" />
<p>Abe’s and Cale’s apartment buildings are exactly the same height. Abe measures the distance between the buildings as 51 m and observes that the angle of depression from the roof of her building to the bottom of Cale’s is about 64°. How tall, to the nearest metre, is each building?</p><img src="/qimages/2286" />
<p>Refer to question 1. Find the tangent of the other acute angle, to four decimal places.</p>
<p>Determine the acute angle at which <code class='latex inline'>y=2x-1</code> and <code class='latex inline'>y=0.5x+2</code> intersect.</p>
<p>What is the relationship between the sine and cosine of complementary angles? Explain your reasoning and use the relationship to find <code class='latex inline'>\displaystyle \cos 50 </code> if <code class='latex inline'>\displaystyle \sin 40 \approx 0.64 . </code></p>
<p>Find <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code>.</p><img src="/qimages/104284" />
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for each triangle, expressed as fractions in lowest terms.</p><img src="/qimages/22886" />
<p>Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65414" />
<p>Find the length of x, then the length of y, to the nearest tenth of a centimetre.</p><img src="/qimages/6776" />
<p>In order to measure the height of a building, Kelly has calculated that its shadow is 23 m long and that the line joining the top of the building to the tip of the shadow forms an angle of <code class='latex inline'>47^{\circ}</code> with the flat ground.</p><p>a) Draw a diagram to illustrate this problem.</p><p>b) Find the height of the building, to the nearest tenth of a metre.</p>
<p>Solve for each angle, to the nearest degree.</p><p><code class='latex inline'>\sin \theta = 0.8872</code></p>
<p>Find <code class='latex inline'>\sin\theta</code>, <code class='latex inline'>\cos\theta</code>, and <code class='latex inline'>\tan \theta</code> for the angle, expressed as fractions in lowest terms.</p><img src="/qimages/22858" />
<p>Using trigonometry, calculate the measures of <code class='latex inline'>\angle A</code> and <code class='latex inline'>\angle B</code> in each triangle. Round your answers to the nearest degree.</p><p> <img src="/qimages/1038" /></p>
<p>Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.</p><img src="/qimages/9475" />
<p>Explain why the value of <code class='latex inline'>\tan\theta</code> increases as the measure of <code class='latex inline'>\theta</code> increases.</p><img src="/qimages/1029" />
<p>What is the value of <code class='latex inline'>\displaystyle \tan x ? </code></p><img src="/qimages/104275" /><p><code class='latex inline'>\displaystyle \begin{array}{ll}\text { A } \tan x=\frac{13}{5} & \text { C } \tan x=\frac{5}{13} \ B \tan x=\frac{12}{5} & \text { D } \tan x=\frac{5}{12}\end{array} </code></p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan \theta = \dfrac{21}{32}</code></p>
<p>A vertical communications tower is supported by two cables on opposite sides of the tower, as shown in the diagram. One cable is attached to the top of the tower and the other is attached to the tower at a height of 60 m. Both cables are attached to the ground with fasteners.</p><img src="/qimages/9401" /><p>a) Verify that <code class='latex inline'>\triangle</code> ABC is similar to <code class='latex inline'>\triangle EBD</code> and list the corresponding sides and angles.</p><p>b) What is the height of the tower, to the nearest metre?</p><p>c) How long are the supporting cables, to the nearest metre?</p><p>d) How far apart are the cable fasteners, to the nearest metre?</p><p>Note: This is a simplified diagram. Normally it takes three or four cables to support a tower.</p>
<p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.303 </code></p>
<p>Nancy and Jordan are looking at the top of the same flagpole. They are standing in a line on the same side of the flagpole, 50.0 m apart. The angle of elevation to the top of the pole is <code class='latex inline'>11^o</code> from Jordan position and and <code class='latex inline'>7^o</code> from Nancy&#39;s position. The girls’ eyes are 1.7 m above ground. For each question, round your answer to the nearest tenth of a metre.</p><p>a) How tall is the flagpole?</p><p>b) How far is each person from the base of the flagpole?</p><p>c) If Nancy and Jordan were standing in a line on opposite sides of the pole, how tall would the flagpole be? How far would each person be from its base?</p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 37^{\circ} </code></p>
<p>Determine all unknown sides to the nearest unit and all unknown interior a angles to the nearest degree.</p><img src="/qimages/2281" />
<p>If the value of <code class='latex inline'>\sin \theta = \frac{2}{5}</code>, find the length of adjacent to <code class='latex inline'>\theta</code> if the opposite side to <code class='latex inline'>\theta</code> is 8. Leave your answer in exact value.</p>
<p>In <code class='latex inline'>\triangle DEF</code>, find <code class='latex inline'>\angle F</code>, to the nearest degree, if <code class='latex inline'>DE = 15 cm</code>, <code class='latex inline'>DF = 18 cm</code>, and <code class='latex inline'>\angle E = 90^o</code>.</p>
<p>Find the measure of both acute angles in each triangle, to the nearest degree.</p><img src="/qimages/5478" />
<p>Determine each unknown value. Round your answer to one decimal place.</p><p>a) <code class='latex inline'>\sin 28^o = \frac{x}{5}</code></p><p>b) <code class='latex inline'>\cos 43^o = \frac{13}{y}</code></p><p>c) <code class='latex inline'>\tan A = 7.1154</code></p><p>d) <code class='latex inline'>\cos B = \frac{7}{9}</code></p>
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 71^{\circ}</code></p>
<p>Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.</p><img src="/qimages/104242" />
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \tan 5^{\circ} </code></p>
<p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos \mathrm{P}=0.731 </code></p>
<p>REASONING Are the values of sine and cosine for an acute angle of a right triangle always less than 1 ? Explain.</p>
<p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.503 </code></p>
<p>CHALLENGE Solve <code class='latex inline'>\displaystyle \triangle A B C </code>. Round to the nearest whole number.</p><img src="/qimages/104270" />
<p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104229" />
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for each triangle, expressed as fractions in lowest terms.</p><img src="/qimages/22887" />
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 19^{\circ} </code></p>
<p>Determine x to one decimal place.</p><p><code class='latex inline'>\displaystyle \cos 29^o = \frac{17.3}{x} </code></p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos S = \dfrac{17}{20}</code></p>
<p>Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65431" />
<p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104224" />
<p>Use the definitions of sine, cosine, and tangent to simplify each expression.</p><p><code class='latex inline'>\displaystyle \begin{array}{lll}\text { a. } \cos A \cdot \tan A & \text { b. } \sin A \div \tan A & \text { c. } \sin A \div \cos A\end{array} </code></p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\cos H = \dfrac{8}{13}</code></p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a centimetre.</p><img src="/qimages/5473" />
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65228" />
<p>To get to school, Eli can travel 1.2 km east on Rutherford St. and then south on Orchard Av. to his school. Or, he can take a shortcut through the park, as shown. His shortcut takes him 20 min.</p><p>Eli&#39;s walking speed is 6 km/h.</p><p>a) What angle does Eli shortcut make with Rutherford st.? Describe any assumptions you must make.</p><p>b) How much time does Eli save by taking his shortcut?</p><img src="/qimages/4025" />
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/22889" />
<p> In a circle O with radius 6, <code class='latex inline'>\angle AOB = 60^{\circ}</code> and <code class='latex inline'>\angle COD = 90^{\circ}</code>. Find the difference in the lengths of line segments CD and AB. Leave your answer in exact value.</p>
<p>Calculate <code class='latex inline'> \sin T </code> in each triangle. Then, find <code class='latex inline'> \angle \mathrm{T} </code> , to the nearest degree.</p><img src="/qimages/65302" />
<p>Solve each of the following triangles. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.</p><img src="/qimages/22873" />
<p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65387" />
<p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>8^{\circ}</code></p>
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6490" />
<p>For <code class='latex inline'>\displaystyle \triangle F G H </code> and <code class='latex inline'>\displaystyle \triangle L M N </code>, find the value of each expression.</p><img src="/qimages/60806" /><p><code class='latex inline'>\displaystyle \cos F </code></p>
<p>The tips of the shadows of a short-wave radio antenna and a 2.5-m tree meet at the point C. The following measurements are taken:</p><p>VB = 7.4 m</p><p>BC = 3.8 m</p><p>Use this information to find the height of the short-wave radio antenna, to the nearest tenth of a metre.</p><img src="/qimages/22879" />
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 82^{\circ}</code></p>
<p>Calculate the length of AB using the information provided. Show all your steps.</p><img src="/qimages/9930" />
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin T = 0.4568</code></p>
<p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22846" />
<p>Find the length of x, to the nearest tenth of a unit.</p><img src="/qimages/9464" />
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 62^{\circ}</code></p>
<p> Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65419" />
<p>Decide whether each statement is true or false. Justify your decision.</p><p><code class='latex inline'>\sin \theta = 0.4</code></p><img src="/qimages/1023" />
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 30^{\circ} </code></p>
<p>The resulting value of <code class='latex inline'>\sin, \cos, \tan</code> of an angle could be? (circle all that could be true)</p><p><code class='latex inline'> \begin{array}{cccccc} &(a) &\text{Angle } &(b)& \text{ decimal } &(c)& \text{ ratio }\\ &(d) & \text{ speed } &(e)& \text{ distance } \\ \end{array} </code></p>
<p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos P=0.621 </code></p>
<p>Solve the triangle</p><p>In <code class='latex inline'>\triangle DEF, \angle F = 90^o, d = 7.8 mm</code>, and <code class='latex inline'>e = 6.9 mm</code>.</p>
<p> The side adjacent to the <code class='latex inline'> 74^{\circ} </code> angle in a right triangle is <code class='latex inline'> 6 \mathrm{~cm} </code> long. How long is the hypotenuse, to the nearest tenth of a centimetre?</p>
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 40^{\circ}</code></p>
<p>In the diagram, <code class='latex inline'>\triangle ABC</code> is isosceles, with <code class='latex inline'>AB = AC</code>, and <code class='latex inline'>\triangle RST</code> is equilateral. Express <code class='latex inline'>\angle x</code> in terms of <code class='latex inline'>\angle y</code> and <code class='latex inline'>\angle z</code></p><img src="/qimages/5597" />
<p>Evaluate the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 35^o</code></p>
<p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65384" />
<p>Give an example of a rational number</p><p>that is not an integer.</p>
<p>A stairway runs up the edge of the pyramid. From bottom to top the stairway is <code class='latex inline'>92</code> m long.</p><img src="/qimages/5488" /><p>The stairway makes an angle of 70° to the base edge, as shown. A line from the middle of one of the base edges to the top of the pyramid makes an angle of elevation of 52° with respect to the flat ground. Find the height of the pyramid.</p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a unit.</p><img src="/qimages/5480" />
<p>Solve <code class='latex inline'>\triangle PQR</code>. Express lengths to the nearest tenth of a centimetre and angles to the nearest degree.</p><img src="/qimages/6966" />
<p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>41.2^{\circ}</code></p>
<p>Calculate <code class='latex inline'>\sin T</code> in each triangle. Then, find <code class='latex inline'>\angle T</code>, to the nearest degree.</p><img src="/qimages/6754" />
<p>Find the measure of <code class='latex inline'>\angle B</code>, to the nearest degree.</p><img src="/qimages/22884" />
<p>Find the measure of each angle to the nearest tenth of a degree using the Distance Formula and an inverse trigonometric ratio. <code class='latex inline'>\displaystyle \angle A </code> in right triangle <code class='latex inline'>\displaystyle A B C </code> with vertices <code class='latex inline'>\displaystyle A(3,1), B(3,-3) </code>, and <code class='latex inline'>\displaystyle C(8,-3) </code></p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan \theta = 0.7128</code></p>
<p>Find <code class='latex inline'> \angle W </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan W=\frac{4}{5} </code></p>
<p>Find x , to the nearest tenth of a centimetre.</p><img src="/qimages/65388" />
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\sin H = 0.9231</code></p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \tan 82^{\circ} </code></p>
<p>Devin wants to estimate the slope of the road near his apartment building. He uses a level that is 1.2 m long and holds it horizontally with one end touching the ground and the other end 39 cm above ground.</p><p>a) What is the slope of the road, to the nearest tenth, at this point?</p><p>b) What angle, to the nearest degree, would represent the slant of the road?</p>
<p>GRIDDED RESPONSE If <code class='latex inline'>\displaystyle A C=12 </code> and <code class='latex inline'>\displaystyle A B=25 </code>, what is the measure of <code class='latex inline'>\displaystyle \angle B </code> to the nearest tenth?</p><img src="/qimages/104280" />
<p>For <code class='latex inline'>\displaystyle \triangle F G H </code> and <code class='latex inline'>\displaystyle \triangle L M N </code>, find the value of each expression.</p><img src="/qimages/60806" /><p><code class='latex inline'>\displaystyle \tan G </code></p>
<p>Nadine has designed a dock in the shape of a right triangle with side lengths 3 m, 4 m, and 5 m. If he enlarges the dock to a similar shape whose side lengths are doubled, what will the area of the new dock be?</p>
<p>Solve the triangle</p><p>In <code class='latex inline'>\triangle ABC, \angle A = 90^o, \angle B = 14^o</code>, and <code class='latex inline'>b = 5.3 cm</code>.</p>
<p>Predict the order, from tallest to shortest, of these famous landmarks_ Then use the given information to determine the actual heights to the nearest metre.</p> <ul> <li>Leaning Tower of Pisa, Pisa, Italy The distance from a point on the ground to the tallest tip of the tower is 81 m with an angle of elevation of <code class='latex inline'>44^o</code></li> </ul>
<p>The pair of triangles is similar. Find the unknown side lengths.</p><img src="/qimages/22877" />
<p> Given that <code class='latex inline'>\angle B = 90^{\circ}</code> and <code class='latex inline'>\cot C = \frac{5}{6}</code> in <code class='latex inline'>\triangle ABC</code>, find the side BC if <code class='latex inline'>AC = 5\sqrt{61}</code>. Leave your answer in exact value.</p>
<p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.101 </code></p>
<p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22843" />
<p>Solve for <code class='latex inline'>x</code>, and express your answer to one decimal place.</p><p> <code class='latex inline'>\tan75^{\circ}=\displaystyle{\frac{x}{20}}</code></p>
<p>Find <code class='latex inline'>\displaystyle x </code>. Round to the nearest tenth.</p><img src="/qimages/104227" />
<p>Find <code class='latex inline'> \angle \mathrm{P} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos P=0.887 </code></p>
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 87^{\circ}</code></p>
<p>Solve for <code class='latex inline'>\angle A</code> to the nearest degree.</p><p><code class='latex inline'>\sin A=0.9063</code></p>
<p>Find the measure of both acute angles in the triangle, to the nearest degree.</p><img src="/qimages/9460" />
<p>Determine the diameter of the circle, if <code class='latex inline'>O</code> is the centre of the circle.</p><img src="/qimages/1046" />
<p>Find the missing values: <strong>a</strong> and <strong>b</strong>. Leave your answer in exact value.</p><img src="/qimages/249" />
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6751" />
<p>Use a special right triangle to express each trigonometric ratio as a fraction and as a decimal to the nearest hundredth. <code class='latex inline'>\displaystyle \tan 45^{\circ} </code></p>
<p>In a right triangle, the side opposite the <code class='latex inline'> 53^{\circ} </code> angle is <code class='latex inline'> 4 \mathrm{~cm} </code> long. How long is the side adjacent to the <code class='latex inline'> 53^{\circ} </code> angle, to the nearest centimetre?</p>
<p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. </p><p><code class='latex inline'>\displaystyle 6 \sqrt{3}, 14,17 </code></p>
<p> Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\displaystyle \begin{array}{llll} &a) & \sin \theta = 0.8933 &b) & \sin \theta = 0.5032\\ &c) & \sin P = \frac{1}{2} &d) & \sin S = \frac{2}{3}\\ &e) & \sin \theta = \frac{3}{4} &f) & \sin A = 0.9511\\ &g) & \sin \theta = 0.7123 &h) & \sin \theta = \frac{2}{5} \\ &i) & \sin X = 0.3035 &j) & \sin \theta = 0.9976 \\ &k) & \sin V = \frac{1}{8} &l) & \sin \theta = 0 \end{array} </code></p>
<p>Calculate sin <code class='latex inline'> \mathrm{T} </code> in each triangle. Then, find <code class='latex inline'> \angle \mathrm{T} </code> , to the nearest degree.</p><img src="/qimages/65301" />
<p>The guy wire to an antenna is 15 m long. The angle the guy wire makes with the ground is <code class='latex inline'>48^{\circ}</code>. Find the height of the antenna, to the nearest tenth of a metre.</p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan R = 3.1478</code></p>
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6748" />
<ol> <li>In <code class='latex inline'>\displaystyle \triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ} . </code> If <code class='latex inline'>\displaystyle \mathrm{AB}=10 \mathrm{~cm} </code> and <code class='latex inline'>\displaystyle \angle \mathrm{C}=38^{\circ} </code>, find the length of <code class='latex inline'>\displaystyle \mathrm{AC} </code>, to the nearest tenth of a centimetre.</li> </ol>
<p>SAT/ACT The area of a right triangle is 240 square inches. If the base is 30 inches long, how many inches long is the hypotenuse?</p><p><code class='latex inline'>\displaystyle \begin{array}{ll}\text { A } 5 & \text { D } 2 \sqrt{241} \ \text { B } 8 & \text { E } 34 \ \text { C } 16 & \end{array} </code></p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 89^{\circ} </code></p>
<p>The corresponding sides of two similar triangles are <code class='latex inline'>\displaystyle 4 \mathrm{~cm} </code> and <code class='latex inline'>\displaystyle 6 \mathrm{~cm} </code> in length. Find the ratio of the areas of the triangles.</p>
<p>Draw two pentagons that are congruent.</p>
<p>Pilots use a “wind triangle&quot; to determine which way to aim the a1r&#39;craft to overcome the effects of wind. For example, Seymour has an airp&#39;lane that cruises at 200 km/h m&#39; still an. A stiff wind of 28 km/h is blowing from the west. Seymour wants to fly from A directly north to B.</p><p>a) Find the angle at which Seymour must aim the airplane.</p><p>b) How fast will he be flying relative to the ground?</p>
<p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the cosine ratio.</p><img src="/qimages/22871" />
<p>In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>AB = 19</code> m, <code class='latex inline'>BC = 27</code> m </p><p><code class='latex inline'>\angle B =</code> 90°</p><p>a) Draw this triangle and label the given information.</p><p>b) Solve <code class='latex inline'>\triangle ABC</code>. Express lengths to the nearest metre and angles to the nearest degree.</p>
<p>Find <code class='latex inline'> \angle \mathrm{Q} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos Q=\frac{15}{16} </code></p>
<p> Find <code class='latex inline'> \sin A </code> and <code class='latex inline'> \sin C </code> in each triangle. Round answers to the nearest thousandth, if necessary.</p><img src="/qimages/65257" />
<p>Dennis has let out <code class='latex inline'>40 m</code> of his kite string, which makes an angle of <code class='latex inline'>72^o</code> with the horizontal ground.</p><img src="/qimages/4024" /><p>a) Find the height of the kite, to the nearest metre.</p><p>b) Suppose the Sun is shining directly above the kite. How far is the kite&#39;s shadow from Dennis, to the nearest meter?</p>
<p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{7}{9} </code></p>
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6961" />
<p>The vertices of <code class='latex inline'>\triangle</code> DEF are D (-3, 11), E (1, -1), and F (7, 9). </p><p>a) Determine the length of each side of this triangle.</p><p>b) Classify the triangle.</p><p>c) Determine the perimeter of the trianglea, Round your answer to the nearest tenth of a unit. </p>
<p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p>tan <code class='latex inline'>52^{\circ}</code></p>
<p> In a right triangle, the side adjacent to an angle of <code class='latex inline'> 23^{\circ} </code> is <code class='latex inline'> 12 \mathrm{~cm} </code> long. How long is the side opposite the <code class='latex inline'> 23^{\circ} </code> angle, to the nearest tenth of a centimetre?</p>
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a metre. </p><img src="/qimages/2385" />
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a metre.</p><img src="/qimages/65223" />
<p>Compare the values of <code class='latex inline'>\sin 30^o</code> and <code class='latex inline'>\cos 60^o</code>. Explain your results using the definition of the two ratios.</p>
<p>For <code class='latex inline'>\displaystyle \triangle F G H </code> and <code class='latex inline'>\displaystyle \triangle L M N </code>, find the value of each expression.</p><img src="/qimages/60806" /><p><code class='latex inline'>\displaystyle \cos L </code></p>
<p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104239" />
<p>Use trigonometric ratios to verify that <code class='latex inline'>\displaystyle \tan \mathrm{A}=\frac{\sin \mathrm{A}}{\cos \mathrm{A}} </code>.</p>
<p>From Tony’s seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard that is 2.1 m above ground. What is the angle of elevation, to the nearest degree, to the top of the blackboard from Tony’s eyes?</p>
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 8^{\circ}</code></p>
<p>Determine each ratio, and write it as a decimal to four decimal places.</p><p><strong>a)</strong> <code class='latex inline'>\sin C</code></p><p><strong>b)</strong> <code class='latex inline'>\cos C</code></p><p><strong>c)</strong> <code class='latex inline'>\tan B</code></p><p><strong>d)</strong> <code class='latex inline'>\tan C</code></p><p><strong>e)</strong> <code class='latex inline'>\cos B</code></p><p><strong>f)</strong> <code class='latex inline'>\sin B</code></p><img src="/qimages/2409" />
<p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{2}{5} </code></p>
<p>Find the perimeter and area of each triangle. Round to the nearest hundredth.</p><img src="/qimages/104256" />
<p> Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65418" />
<p>Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. </p><p><code class='latex inline'>\displaystyle 13,30,35 </code></p>
<p>Find the length of the unknown side, to the nearest tenth.</p><img src="/qimages/22850" />
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan A = 0.5123</code></p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a metre.</p><img src="/qimages/22883" />
<p>Find <code class='latex inline'> \angle \mathrm{J} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin J=0.952 </code></p>
<p>Solve the triangle. Round lengths to the nearest unit and angle measures to the nearest degree.</p><img src="/qimages/9428" />
<p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22844" />
<p>During a football game, Danny, the quarterback, has the football and is facing the other team’s goal line. His receiver, Javier, is about <code class='latex inline'>5.5</code> m to Danny’s left, at an angle of 30°, as shown.</p><img src="/qimages/5485" /><p>How far should Danny throw the ball to his receiver, to the nearest metre?</p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \tan 62^{\circ} </code></p>
<p>A kite string is 35 m long. The angle the string makes with the ground is 50°. To the nearest metre, how far from the person holding the string is a person standing directly under the kite?</p><img src="/qimages/6772" />
<p>Explain how you would determine the measurement of the indicated angle or side in each triangle.</p><img src="/qimages/1609" />
<p>Find tan <code class='latex inline'> A </code> and tan <code class='latex inline'> C </code> in each triangle. Round answers to the nearest thousandth, if necessary</p><img src="/qimages/65177" />
<p>Solve using trigonometric ratios. </p><p>A right triangle&#39;s legs are 7 in. and 24 in. long. What is the measure of the angle opposite the 24 -in. leg?</p>
<p>Find the measure of each angle, to the nearest degree.</p><p>tan S = <code class='latex inline'>\dfrac{11}{3}</code></p>
<p>Describe the difference between finding the sine of an angle and the cosine of an angle.</p>
<p>Find all the unknown angles, to the nearest degree, and all the unknown side lengths, to the nearest tenth of a unit.</p><img src="/qimages/65428" />
<p>Evaluate with a calculator. Round your answer to the nearest ten thousandth.</p><p><code class='latex inline'>\tan 78.4^{\circ}</code></p>
<p>Solve each triangle. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.</p><img src="/qimages/22890" />
<p>Solve each right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.</p><img src="/qimages/104244" />
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6493" />
<p>Find <code class='latex inline'>\displaystyle \angle \mathrm{B} </code>, to the nearest degree.</p><p><code class='latex inline'>\displaystyle \tan B=0.833 </code></p>
<p>Determine the length of <code class='latex inline'>x</code>. Then state the primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p> <img src="/qimages/1026" /></p>
<p>Draw two squares that are similar.</p>
<p>Solve each of the following triangles. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.</p><img src="/qimages/22872" />
<p>The pair of triangles is similar. Find the unknown side lengths.</p><img src="/qimages/22878" />
<p>Find <code class='latex inline'> \angle \mathrm{B} </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \sin B=\frac{1}{8} </code></p>
<p>Find <code class='latex inline'>\sin \theta</code>, <code class='latex inline'>\cos \theta</code>, and <code class='latex inline'>\tan \theta</code> for the triangle, expressed as fractions in lowest terms.</p><img src="/qimages/6491" />
<p>Solve for <code class='latex inline'>t</code>. Round answers to two decimal places.</p><p><code class='latex inline'>\displaystyle 10 = (\frac{1}{4})^{{3t} </code></p>
<p>Find the value of <code class='latex inline'>x</code> to the nearest tenth. </p><img src="/qimages/60828" />
<p>Solve using trigonometric ratios. </p><p>A right triangle has a <code class='latex inline'>\displaystyle 40^{\circ} </code> angle. The hypotenuse is <code class='latex inline'>\displaystyle 10 \mathrm{~cm} </code> long. What is the length of the side opposite the <code class='latex inline'>\displaystyle 40^{\circ} </code> angle?</p>
<p>The maximum angle of climb for a certain light aircraft is 9°. A line of electric wires <code class='latex inline'>20</code> m above the ground is located <code class='latex inline'>120</code> m from the end of the runway. Will the aircraft clear the wires after take-off?</p>
<p>Find the measure of each angle, to the nearest degree.</p><p><code class='latex inline'>\tan Q = 1.2</code></p>
<p>Calculate <code class='latex inline'> \cos \mathrm{T} </code> in each triangle. Then, find <code class='latex inline'> \angle \mathrm{T} </code> , to the nearest degree.</p><img src="/qimages/65380" />
<p>Rachel is heading due south in her sailboat toward a port. After travelling <code class='latex inline'>12</code> km, she reaches shore <code class='latex inline'>4</code> km west of her intended destination, due to the water’s current. By what angle did the current push Rachel off course? Include a diagram in your solution and describe any assumptions you must make.</p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \cos 83^{\circ} </code></p>
<p>Use a calculator to find the measure of <code class='latex inline'>\displaystyle \angle T </code> to the nearest tenth.</p><img src="/qimages/104236" />
<p>Find the length of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/6958" />
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\sin 38^{\circ}</code></p>
<ol> <li>Calculate tan <code class='latex inline'>\displaystyle D, \angle D, \tan E </code>, and <code class='latex inline'>\displaystyle \angle E </code>. Round each angle measure to the nearest degree.</li> </ol> <img src="/qimages/65211" />
<p>Find the value of <code class='latex inline'>x</code>, to the nearest tenth of a unit, by applying the sine ratio.</p><img src="/qimages/22865" />
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65306" />
<p>The towrope pulling a parasailor is 70 m long. A boat crew member estimates that the angle between the towrope and the water is about 30°. Find the height of the parasailor above the water.</p>
<p>Find <code class='latex inline'> \angle Q </code> , to the nearest degree.</p><p><code class='latex inline'>\displaystyle \cos \mathrm{Q}=\frac{7}{8} </code></p>
<p>Solve each triangle. Round each side length to the nearest tenth of a unit, and each angle to the nearest degree.</p><img src="/qimages/65410" />
<p>Given the regular pentagon shown at the left, determine its perimeter to the nearest tenth of a centimetre and its area to the nearest tenth of a square centimetre.</p><img src="/qimages/165740" />
<p>A jet climbs at a steady rate at an angle of inclination of <code class='latex inline'>0.5^o</code> during take-off. What will its height be after a <code class='latex inline'>2.2</code>-km initial ascent at this angle?</p>
<p>Solve for <code class='latex inline'>x</code>, and express your answer to one decimal place.</p><p> <code class='latex inline'>\cos45^{\circ}=\displaystyle{\frac{x}{6}}</code></p>
<p>Sam wants to find the height of a tree without having to climb it, but it is a cloudy day, so he cannot use shadows. He takes a mirror from his pocket and places it on the ground <code class='latex inline'>7.2</code> m from the base of the tree. He backs up until he can see the top of the tree in the mirror, a distance of <code class='latex inline'>1.2</code> m from the mirror. If Sid’s eyes are <code class='latex inline'>1.5</code> m above the ground, what is the height of the tree?</p>
<p>Find <code class='latex inline'>x</code>, to the nearest tenth of a unit.</p><img src="/qimages/5482" />
<p><strong>a)</strong> Which side is opposite to <code class='latex inline'>\angle A</code>?</p><p><strong>b)</strong> Which side is adjacent to <code class='latex inline'>\angle A</code>?</p><p><strong>c)</strong> Which side is the hypotenuse? </p><img src="/qimages/2408" />
<p>Determine the length of <code class='latex inline'>x</code>. Then state the primary trigonometric ratios for <code class='latex inline'>\theta</code>.</p><p> <img src="/qimages/1027" /></p>
<p>Find the tangent of the angle indicated, to four decimal places.</p><img src="/qimages/22841" />
<p>Find the value of <code class='latex inline'> x </code> , to the nearest tenth of a centimetre.</p><img src="/qimages/65312" />
<p>In <code class='latex inline'>\triangle TUV, UV = 7.4 km, \angle U = 90^o, \angle T = 38^o</code></p><p>a) Draw the triangle and label the given information.</p><p>b) Solve <code class='latex inline'>\triangle TUV</code></p>
<p>A coast guard patrol boat is 14.8 km east of the Brier Island lighthouse. A disabled yacht is 7.5 km south of the lighthouse.</p><p>a) How far is the patrol boat from the yacht, to the nearest tenth of a kilometre?</p><p>b) At what angle south of due west, to the nearest degree, should the patrol boat travel to reach the yacht?</p>
<p>Each side length of regular pentagon <code class='latex inline'>ABCDE</code> is 8.2 cm.</p><p> Calculate the length of diagonal <code class='latex inline'>AC</code> to the nearest tenth of a centimetre.</p><img src="/qimages/1054" />
<p>Evaluate each of the following with a calculator, rounded to four decimal places.</p><p><code class='latex inline'>\cos 68^{\circ}</code></p>
<p>Kathy is <code class='latex inline'>4</code> m from the base of a long wooden fence, under which her baseball has just rolled. Kathy estimates that the angle of elevation from where she is to the top of the fence is about <code class='latex inline'>30^o</code>. Kathy thinks she can climb over a fence that is a maximum of <code class='latex inline'>2</code> m high. Can she climb over the fence, or does she have to go around? Justify your reasoning.</p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \sin 60^{\circ} </code></p>
<p>Find each of the following, to the nearest thousandth.</p><p><code class='latex inline'>\displaystyle \tan 15^{\circ} </code></p>
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