Now You Try

<p> Find the indicated side <code class='latex inline'>x</code> or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1515" />

<p>Calculate each unknown angle to the nearest degree and each unknown In length to the nearest tenth of a centimetre.</p><img src="/qimages/929" />

<p>Calculate each unknown angle to the nearest degree and each unknown In length to the nearest tenth of a centimetre.</p><img src="/qimages/928" />

<p>Charles leaves the marina and sails his boat <code class='latex inline'>10^o</code> west of north for 1.5 h at 18 km/h. He then makes a starboard (right) turn to a heading of <code class='latex inline'>60^o</code> east of north, and sails for 1.2 h at 20 km/h.</p><p>At the end of that time, how far is Charles from his starting point to the nearest kilometre?</p>

<p>For each triangle, determine the value of <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/922" />

<p>Two hot-air balloons are moored to level ground below, each at a different location. An observer at each location determines the angle of elevation to the opposite ballon as shown at the right. The observers are 2.0 km apart.</p><p>(a) What is the distance separating the balloons, to the nearest tenth of a kilometre?</p><img src="/qimages/932" />

<p> Find the area of the shaded figure, correct to two decimals.</p><img src="/qimages/1519" />

<p>Select the most appropriate trigonometric tools among primary trigonometric ratios, the sine law, and the cosine law. Justify your choice. Do not solve.</p><p>In <code class='latex inline'>\triangle XYZ, \angle X = 42^o, y = 25 km</code>, and z = 20km. Determine x.</p>

<p>Two forest fire towers, <code class='latex inline'>A</code> and <code class='latex inline'>B</code>, are 20.3 km apart. From tower <code class='latex inline'>A</code>, the bearing of tower <code class='latex inline'>B</code> is <code class='latex inline'>70^{\circ}</code>. The ranger in each tower observes a fire and radios the bearing of the fire from the tower. The bearing from tower A is <code class='latex inline'>25^{\circ}</code> and from tower <code class='latex inline'>B</code> is <code class='latex inline'>345^{\circ}</code>. How far, to the nearest tenth of a kilometre, is the fire from each tower? </p>

<p> Find the area of the shaded figure, correct to two decimals.</p><img src="/qimages/1521" />

<p> Find the area of the triangle whose sides have the given lengths.</p>
<ul>
<li><code class='latex inline'>a = 7, b = 8, c = 9</code></li>
</ul>

<p> Find the indicated side <code class='latex inline'>x</code> or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1517" />

<p>Determine each unknown side length to the nearest tenth.</p><img src="/qimages/921" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1510" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1511" />

<p> To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information.</p><img src="/qimages/1523" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1513" />

<p>A decorative pottery bowl with a diameter of 30 cm is used as a garden ornament. A rain shower fills it with water to a maximum depth of 7 cm. The bowl is slowly tipped to remove the water. What angle will the rim of the bowl make with the horizontal when the water begins to spill out?</p>

<p> Find the area of the triangle whose sides have the given lengths.</p>
<ul>
<li><code class='latex inline'>a = 11, b = 100, c = 101</code></li>
</ul>

<p> Find the indicated side <code class='latex inline'>x</code> or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1516" />

<p>The posts of a hockey goal are 2.0 m apart. A player attempts to score by shooting the puck along the ice from a point 6.5 m from one post and 8.0 m from the other. Within what angle <code class='latex inline'>\theta</code> must the shot be made? Round your answer to the nearest degree.</p><img src="/qimages/930" />

<p>Determine <code class='latex inline'>w</code> to the nearest tenth.</p><img src="/qimages/924" />

<p>Two hot-air balloons are moored to level ground below, each at a different location. An observer at each location determines the angle of elevation to the opposite ballon as shown at the right. The observers are 2.0 km apart.</p><p>Determine the difference in height (above the ground) between the two balloons. Round your answer to the nearest metre.</p><img src="/qimages/932" />

<p>Given <code class='latex inline'>\Delta ABC</code> below, <code class='latex inline'>BC = 2.0</code> and <code class='latex inline'>D</code> is the midpoint of <code class='latex inline'>BC</code>. Determine <code class='latex inline'>AB</code>, to the nearest tenth, if <code class='latex inline'>\angle ADB = 45^{\circ}</code> and <code class='latex inline'>\angle ACB = 30^{\circ}</code>.</p><img src="/qimages/22167" />

<p> Find the area of the shaded figure, correct to two decimals.</p><img src="/qimages/1522" />

<p>Determine <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/925" />

<p>For each triangle, determine the value of <code class='latex inline'>\theta</code> to the nearest degree.</p><img src="/qimages/923" />

<p>For each situation, determine all unknown side lengths to the nearest tenth of a centimetre and/or all unknown interior angles to the nearest degree. If more than one solution is possible, state all possible answers.</p><p>(a) A triangle has exactly one angle measuring <code class='latex inline'>45^o</code> and sides measuring 5.0 cm, 7.4 cm, and 10.0 cm.</p>

<p>Determine each unknown side length to the nearest tenth.</p><img src="/qimages/920" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1512" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1509" />

<p>While golfing, Sean hits a tee shot from <code class='latex inline'>T</code> toward a hole at <code class='latex inline'>H</code>, but the ball veers <code class='latex inline'>23^{\circ}</code> and lands at <code class='latex inline'>B</code>. The scorecard says that <code class='latex inline'>H</code> is 270 m from <code class='latex inline'>T</code>. If Sean walks 160 m to the ball (B), how far, to the nearest metre, is the ball from the hole?</p><img src="/qimages/931" />

<p>Use the Law of Cosines to determine the indicated side x or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1514" />

<p> Find the area of the triangle whose sides have the given lengths.</p>
<ul>
<li><code class='latex inline'>a = 9, b = 12, c = 15</code></li>
</ul>

<p>For each situation, determine all unknown side lengths to the nearest tenth of a centimetre and/or all unknown interior angles to the nearest degree. If more than one solution is possible, state all possible answers.</p><p>(b) An isosceles triangle has at least one interior angle of <code class='latex inline'>70^o</code> and at least one side of length 11.5 cm.</p>

<p>Calculate each unknown angle to the nearest degree and each unknown In length to the nearest tenth of a centimetre.</p><img src="/qimages/927" />

<p>The interior angles of a triangle are <code class='latex inline'>120^{\circ}</code>, <code class='latex inline'>40^{\circ}</code>, and <code class='latex inline'>20^{\circ}</code>. The longest side is 10 cm longer than the shortest side. Determine the perimeter of the triangle to the nearest centimetre. </p>

<p> Find the area of the triangle whose sides have the given lengths.</p>
<ul>
<li><code class='latex inline'>a = 1, b = 2, c = 2</code></li>
</ul>

<p>Bill and Nadia live across a ravine from each other. Bill rowed 180 m to the end of the ravine, turned right through an angle of <code class='latex inline'>45^o</code>, and walked another <code class='latex inline'>200 m</code> to Nadia's house. Determine an exact expression for the distance between the two houses.</p>

<p>In <code class='latex inline'>\Delta ABC</code>, <code class='latex inline'>a = 11.5</code>, <code class='latex inline'>b = 8.3</code>, and <code class='latex inline'>c = 6.6</code>. Calculate <code class='latex inline'>\angle A</code> to the nearest degree.</p>

<p> Find the area of the shaded figure, correct to two decimals.</p><img src="/qimages/1520" />

<p>In <code class='latex inline'>\Delta PQR</code>, <code class='latex inline'>q = 25.1</code>, <code class='latex inline'>r = 71.3</code>, and <code class='latex inline'>\cos P = \frac{1}{4}</code>. Calculate <code class='latex inline'>p</code> to the nearest tenth.</p>

<p> Find the indicated side <code class='latex inline'>x</code> or angle <code class='latex inline'>\theta</code>.</p><img src="/qimages/1518" />

<p>Determine the indicated unknown quantity:</p><p>In <code class='latex inline'>\triangle XYZ, \angle X = 42^o, y = 25 km</code>, and <code class='latex inline'>z = 20km</code>. Determine <code class='latex inline'>x</code>.</p>

<p>The Leaning Tower of Pisa is 55.9 m tall and leans <code class='latex inline'>5.5^{\circ}</code> from the vertical. If its shadow is 90.0 m long, what is the distance from the top of the tower to the top edge of its shadow? Assume that the ground around the tower is level. Round your answer to the nearest metre.</p>

<p>You receive a scientific calculator at checkpoint num 3. Determine the direction and distance to checkpoint num 4 from the information below. Draw the leg on your map. Include all angles and distances.</p><p><strong>Direction:</strong> North of West</p>
<ul>
<li>Use <code class='latex inline'>\angle A</code> from <code class='latex inline'>\triangle ABC</code>. In <code class='latex inline'>\triangle ABC</code>, <code class='latex inline'>\angle B = 85^o</code>, <code class='latex inline'>a = 41 m</code>, and <code class='latex inline'>c = 32 m</code>. Round to the nearest degree, if necessary. </li>
</ul>
<p><strong>Distance</strong> The measure of <code class='latex inline'>b</code>, in <code class='latex inline'>\triangle ABC</code>, to the nearest metre.</p>

<p>Calculate each unknown angle to the nearest degree and each unknown In length to the nearest tenth of a centimetre.</p><img src="/qimages/926" />