34. Q10
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<p> A <code class='latex inline'> 1.5-\mathrm{m} </code> hoe rests against the side of a garden shed. The angle the handle of the hoe forms with the ground is <code class='latex inline'> 71^{\circ} . </code> How far up the wall of the shed does the hoe reach, to the nearest tenth of a metre?</p><img src="/qimages/65321" />
Similar Question 2
<img src="/qimages/10077" /><p>An <code class='latex inline'>\displaystyle 8.0 \mathrm{~m} </code> ladder is leaning against a vertical wall. The foot of the ladder is <code class='latex inline'>\displaystyle 2.0 \mathrm{~m} </code> from the base of the wall. What is the angle formed by the ladder and the oround? ground?</p><p>A. <code class='latex inline'>\displaystyle 73.7^{\circ} </code></p><p>C. <code class='latex inline'>\displaystyle 75.5^{\circ} </code></p><p>B. <code class='latex inline'>\displaystyle 74.9^{\circ} </code></p><p>D. <code class='latex inline'>\displaystyle 76.6^{\circ} </code></p>
Similar Question 3
<p>Steph is 117 cm tall, and her eyes are 106 cm off the ground. She is using her new binoculars to look at a bird that is perched in a tree. </p><p>The angle of elevation is 28°, and Stephanie is 25.0 m from the base of the tree. What is the height of the bird in the tree?</p><p>A. 13.3 m</p><p>B. 12.8 m</p><p>C. 23.1 m</p><p>D. 14.4 m</p>
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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
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<p>Lucy’s space shuttle is 35 km from her mother ship and 42 km from a space station. From Lucy’s point of View, the mother ship and space station appear to be 49° apart, as shown.</p><img src="/qimages/5713" /><p>a) How far apart are the mother ship and the space station, to the nearest kilometre?</p><p>b) From the space station, by what angle do the shuttle and mother ship appear to be separated, to the nearest degree?</p>
<img src="/qimages/65440" /> <ol> <li>Two CN Towers Edmonton&#39;s CN Tower is a highrise office building. From a point <code class='latex inline'>\displaystyle 35 \mathrm{~m} </code> from the base of the building and level with the base, the angle of elevation of the top is <code class='latex inline'>\displaystyle 72.5^{\circ} </code>.</li> </ol> <p>a) Find the height of Edmonton&#39;s <code class='latex inline'>\displaystyle \mathrm{CN} </code> Tower, to the nearest metre.</p><p>b) Toronto&#39;s <code class='latex inline'>\displaystyle \mathrm{CN} </code> Tower is a tourist attraction, with a height of <code class='latex inline'>\displaystyle 555 \mathrm{~m} </code>. How many times as tall as Edmonton&#39;s <code class='latex inline'>\displaystyle \mathrm{CN} </code> Tower is Toronto&#39;s <code class='latex inline'>\displaystyle \mathrm{CN} </code> Tower?</p><p>c) Communication Edmonton&#39;s CN Tower has 27 storeys. If an office building were the height of Toronto&#39;s <code class='latex inline'>\displaystyle \mathrm{CN} </code> Tower, how many storeys would you expect it to have? Explain.</p>
<p> Two ships left Parry Sound and sailed into Georgian Bay at the same time. One travelled at <code class='latex inline'> 16 \mathrm{~km} / \mathrm{h} </code> on a course of <code class='latex inline'> 277^{\circ} </code> . The other travelled at <code class='latex inline'> 14 \mathrm{~km} / \mathrm{h} </code> on a course of <code class='latex inline'> 230^{\circ} </code> . How far apart were the ships after two hours, to the nearest tenth of a kilometre?</p><img src="/qimages/66364" />
<p>Pietra walked diagonally across a rectangular schoolyard <code class='latex inline'> 45 \mathrm{~m} </code> by <code class='latex inline'> 65 \mathrm{~m} </code> . To the nearest degree, at what angle with respect to the longer side did she walk?</p>
<p>A canoeist starts from a dock and paddles 2.8 km N34°E. Then she paddles 5.2 km N65°W What distance, and in which direction, should a second canoeist paddle to reach the same location directly, starting from the same dock?</p>
<p> Find the volume of the right prism, to the nearest cubic metre.</p><img src="/qimages/66369" />
<p>A flagpole stands on top of a building that is 27 m high. From a point on the ground some distance away, the angle of elevation to the top of the flagpole is 43&quot;. The angle of elevation to the bottom of the flagpole is 32°.</p><p>a) How far is the point on the ground from the base of the building?</p><p>b) How tall is the flagpole?</p>
<p><code class='latex inline'> A </code> tree is splintered by lightning <code class='latex inline'> 2 \mathrm{~m} </code> 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 <code class='latex inline'> 70^{\circ} </code> . Before it was splintered, how tall was the tree, to the nearest tenth of a metre?</p><img src="/qimages/65325" />
<p>An engineer wants to build a bridge over a river from point A to point B as shown in the diagram at the left. The distance from point B to point C is 515.0 m. </p><p>The engineer uses a transit to determine that <code class='latex inline'>\angle B</code> is 72° and <code class='latex inline'>\angle C</code> is 53°. Determine the length of the finished bridge.</p>
<p>A box is in the shape of a square-based prism. The height of the box is twice the width of the base.</p><p><strong>a)</strong> Show that the longest thin rod that can be encased in the box has length <code class='latex inline'>\sqrt{6}w</code>, where <code class='latex inline'>w</code> is the width of the base.</p><p><strong>b)</strong> Find the angles that such a rod would make with each edge of the box.</p>
<p>Ryan is in a police helicopter 400 m directly above a highway. When he looks west, the angle of depression to a car accident is 65°. When he looks east, the angle of depression to the approaching ambulance is 30°.</p> <ul> <li>How far away is the ambulance from the scene of the accident?</li> </ul>
<p>The Nautilus is sailing due east toward a buoy. At the same time, the Porpoise is approaching the buoy heading N42°E. If the Nautilus is 5.4 km from the buoy and the Porpoise is 4.0 km from the Nautilus. on a heading of 546°E, how far is the Porpoise from the buoy?</p>
<img src="/qimages/65399" /><p>Find all the angles in <code class='latex inline'> \triangle W X Y </code> , to the nearest degree.</p><img src="/qimages/65400" />
<p>Two paper strips, each <code class='latex inline'>5 cm</code> wide, are laid across each other at an angle of 30°, as shown at the right. Determine the area of the overlapping region. Round your answer to the nearest tenth of a square centimetre.</p><img src="/qimages/1613" />
<p>The two guy wires supporting a flagpole are each anchored <code class='latex inline'> 7 \mathrm{~m} </code> from the flagpole and form an angle of <code class='latex inline'> 52^{\circ} </code> with the ground. What is the total length of guy wire, to the nearest metre, needed to support this flagpole?</p>
<p>The radar screen in an air—traffic control tower shows that two airplanes are at the same altitude. According to the range finder, one airplane is 100 km away, in the direction N60°E. The other airplane is 160 km away, in the direction S5O°E.</p> <ul> <li>If the airplanes are approaching the airport at the same speed, which airplane will arrive first?</li> </ul>
<img src="/qimages/10077" /><p>An <code class='latex inline'>\displaystyle 8.0 \mathrm{~m} </code> ladder is leaning against a vertical wall. The foot of the ladder is <code class='latex inline'>\displaystyle 2.0 \mathrm{~m} </code> from the base of the wall. What is the angle formed by the ladder and the oround? ground?</p><p>A. <code class='latex inline'>\displaystyle 73.7^{\circ} </code></p><p>C. <code class='latex inline'>\displaystyle 75.5^{\circ} </code></p><p>B. <code class='latex inline'>\displaystyle 74.9^{\circ} </code></p><p>D. <code class='latex inline'>\displaystyle 76.6^{\circ} </code></p>
<img src="/qimages/65443" /> <ol> <li>Communication a) Use right triangles <code class='latex inline'>\displaystyle \mathrm{ABC} </code> and <code class='latex inline'>\displaystyle \mathrm{DEF} </code> to copy and complete the table. Leave all ratios in fraction form.</li> </ol> <p>d) How is <code class='latex inline'>\displaystyle \cos x </code> related to <code class='latex inline'>\displaystyle \sin \left(90^{\circ}-x\right) </code> ? e) Explain the relationships in parts a), b), and c).</p>
<p>The radar screen of a Coast Guard rescue ship shows that two boats are in the area. </p><p>According to the range finder, one boat is 70 km away, in the direction N45°E. The other boat is 100 km away, in the direction S50°E. How far apart are the two boats?</p>
<img src="/qimages/10076" /><p>If <code class='latex inline'>\displaystyle B M=M C </code> and <code class='latex inline'>\displaystyle B C=12 \mathrm{~cm} </code>, what is the value of <code class='latex inline'>\displaystyle x </code> ?</p><p>A. <code class='latex inline'>\displaystyle 9.3 \mathrm{~cm} </code></p><p>B. <code class='latex inline'>\displaystyle 7.8 \mathrm{~cm} </code></p><p>C. <code class='latex inline'>\displaystyle 3.9 \mathrm{~cm} </code></p><p>D. <code class='latex inline'>\displaystyle 18.7 \mathrm{~cm} </code></p>
<p>Greg and Kristen are on opposite ends of a zip line that crosses a gorge. Greg went across the gorge first, and he is now on a ledge that is 15 m above the bottom of the gorge. Kristen is at the top of a cliff that is 72 m above the bottom of the gorge. Jon is on the ground at the bottom of the gorge, below the zip line. He sees Kristen at a 65° angle of elevation and Greg at a 35° angle of elevation. What is the width of the gorge, to the nearest metre?</p><p>A. 165 m</p><p>B. 152 m</p><p>C. 55 m</p><p>D. 106 m</p>
<p> A sign shows that a hill has a grade of <code class='latex inline'> 9 \% </code> . What angle does the hill make with the horizontal, to the nearest tenth of a degree?</p>
<p>Triathlon The three phases of a triathlon involve swimming, cycling, and running, in that order. The distances for each phase can vary. For a triathlon held in Hawaii each year, competitors swim in the ocean, bicycle <code class='latex inline'>\displaystyle 112 \mathrm{~km} </code>, and run <code class='latex inline'>\displaystyle 41.8 \mathrm{~km} </code>. In the diagram, <code class='latex inline'>\displaystyle \mathrm{S} </code> is the</p><p><code class='latex inline'>\displaystyle 2.7 \mathrm{~km} </code> start of the swim, and <code class='latex inline'>\displaystyle \mathrm{F} </code> is the finish. A surveyor used the</p><p>dimensions shown to calculate the length SF across the bay. a) Find the distance the athletes swim in the Hawaiian triathlon,</p><p><code class='latex inline'>\displaystyle 86.9 \% \quad 2.1 \mathrm{~km} </code> to the nearest metre.</p><p>b) Communication What assumptions have you made?</p>
<p>From the top of an 8 m house, the angle of elevation to the top of a flagpole across the street is 9°. The angle of depression is 22° to the base of the flagpole. How tall is the flagpole?</p><img src="/qimages/9944" />
<p>A boat leaves Oakville and heads due east for 5.0 km as shown in the diagram at the left. At the same time, a second boat travels in a direction S60°E From Oakville for 4.0 km. How far apart are the boats when they reach their respective destinations?</p><img src="/qimages/1611" />
<p>A radar operator on a ship discovers a large sunken vessel lying flat on the ocean floor, 200 m directly below the ship. The radar operator measures the angles of depression to the front and back of the sunken ship to be 56° and 62°. How long is the sunken ship?</p>
<p>Fred and Agnes are 520 m apart. As Brendan flies overhead in an airplane, they measure the angle of elevation of the airplane. Fred measures the angle of elevation to be 63°. Agnes measures it to be 36°. What is the altitude of the airplane?</p>
<p>Points P and Q lie 240 m apart on opposite sides of a communications tower. The angles of elevation to the top of the tower from P and Q are 50° and 45°, respectively. Calculate the height of the tower.</p>
<p> A <code class='latex inline'> 1.5-\mathrm{m} </code> hoe rests against the side of a garden shed. The angle the handle of the hoe forms with the ground is <code class='latex inline'> 71^{\circ} . </code> How far up the wall of the shed does the hoe reach, to the nearest tenth of a metre?</p><img src="/qimages/65321" />
<p>A bush pilot delivers supplies to a remote camp by flying 255 km in the direction N52°E. While at the camp, the pilot receives a radio message to pick up a passenger at a village. The village is 85 km 521°E from the camp. What is the total distance that the pilot will have flown by the time he returns to his starting point?</p>
<p>The radar screen in an air—traffic control tower shows that two airplanes are at the same altitude. According to the range finder, one airplane is 100 km away, in the direction N60°E. The other airplane is 160 km away, in the direction S5O°E.</p> <ul> <li>How far apart are the airplanes?</li> </ul>
<p>The base of a roof is 12.8 m wide as shown in the diagram at the left. The rafters form angles of 48° and 44° with the horizontal. How long, to the nearest tenth of a metre, is each rafter?</p>
<p>A ladder leans against a vertical wall and makes an angle of <code class='latex inline'> 65^{\circ} </code> with the ground. The foot of the ladder is <code class='latex inline'> 2 \mathrm{~m} </code> from the base of the wall. Calculate the length of the ladder, to the nearest tenth of a metre.</p><img src="/qimages/65396" />
<ol> <li>Coast guard A coast guard patrol boat is <code class='latex inline'>\displaystyle 14.8 \mathrm{~km} </code> east of the Brier Island lighthouse. A disabled yacht is <code class='latex inline'>\displaystyle 7.5 \mathrm{~km} </code> south of the lighthouse.</li> </ol> <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>Ethan and Tariq want to estimate the area of the field that their team will use for soccer practice. They know that the field is rectangular, and they have paced off the width of the field as shown. They used the fence posts at the corners of the field to estimate that the angle between the length of the field and the diagonal is about <code class='latex inline'>\displaystyle 40^{\circ} </code>. If they assume that each of their steps is about 18 inches, what is the area of the practice field in square feet? Round to the nearest square foot.</p>
<p> Montréal&#39;s Marathon building is <code class='latex inline'> 195 \mathrm{~m} </code> tall. From a point level with, and <code class='latex inline'> 48 \mathrm{~m} </code> from, the base of the building, what is the angle of elevation of the top of the building, to the nearest degree?</p><img src="/qimages/65436" />
<p>Kevin is standing 15 m from the base of a building. From the point where he is standing, the angle of elevation of the top of the building is <code class='latex inline'>32^{\circ}</code>. How tall is the building, to the nearest tenth of a metre?</p>
<p>Lucas is designing a flower garden in the shape of an isosceles right triangle. He has created a scale diagram. The lengths of the perpendicular sides in the scale diagram are 7 cm, and the hypotenuse of the real garden will be 3 m long. What is the area of the real garden?</p><p>A. <code class='latex inline'>450 m^2</code></p><p>B. <code class='latex inline'>2.25 m^2</code></p><p>C. <code class='latex inline'>1033 m^2</code></p><p>D. <code class='latex inline'>4.5 m^2</code></p>
<p>From the top of a bridge that is 50 m high, two boats can be seen anchored in a marina, One boat is anchored in the direction 820°W, and its angle of depression is 40°. The other boat is anchored in the direction 560°E, and its angle of depression is 30°. Determine the distance between the two boats.</p>
<p> The world&#39;s fastest roller coaster is at Six Flags Magic Mountain. At the start, riders are shot forward and then up a tower. They then begin the backward descent. The cars reach a speed of <code class='latex inline'> 160 \mathrm{~km} / \mathrm{h} </code> in <code class='latex inline'> 7 \mathrm{~s} </code> during the descent. From a point <code class='latex inline'> 100 \mathrm{~m} </code> from the foot of the tower, the angle of elevation of the top of the tower is <code class='latex inline'> 52^{\circ} . </code> Find the height of the tower, to the nearest metre.</p>
<p>Leoislookingdown, from the roof of a building, at a dump truck that is parked on the road. The angle of depression to the front of the truck is 58°, and the building is 37 m tall. What is the distance between the base of the building and the front of the truck?</p><p>A. 41 m</p><p>B. 23 m</p><p>C. 59 m</p><p>D. 27 m</p>
<p>Steph is 117 cm tall, and her eyes are 106 cm off the ground. She is using her new binoculars to look at a bird that is perched in a tree. </p><p>The angle of elevation is 28°, and Stephanie is 25.0 m from the base of the tree. What is the height of the bird in the tree?</p><p>A. 13.3 m</p><p>B. 12.8 m</p><p>C. 23.1 m</p><p>D. 14.4 m</p>
<p>Two airplanes leave an airport at the same time. One airplane travels at 355 km/h. The other airplane travels at 450 km/h. About 2 h later, theyare800kmapart.Determine the angle between their paths.</p>
<p>Three billiard balls are lying as shown.</p><img src="/qimages/5716" /><p>The white cue ball is 55 cm from the red ball and 62 cm from the black ball. The line segment from the red ball to the white ball and the line segment from the red ball to the black ball form an angle of 82°.</p><p>a) How far apart are the red and black balls, to the nearest centimetre?</p><p>b) Find the measures of the other angles in the triangle formed by these three billiard balls, to the nearest degree.</p>
<p>Denny and Selena are standing at the points A and B on the opposite sides of a hydro pole. From point A the angle of elevation of the top of the hydro pole is <code class='latex inline'>28^{\circ}</code>, and from point B the angle of elevation of the top of the hydro pole is <code class='latex inline'>34^{\circ}</code>. The hydro pole is 7 m in height. How far apart are Denny and Selena, to the nearest tenth of a metre?</p>
<img src="/qimages/10075" /><p>What is the value of <code class='latex inline'>\displaystyle x ? </code></p><p>A. <code class='latex inline'>\displaystyle 3.00 \mathrm{~cm} </code></p><p>B. <code class='latex inline'>\displaystyle 6.80 \mathrm{~cm} </code></p><p>C. <code class='latex inline'>\displaystyle 9.70 \mathrm{~cm} </code></p><p>D. <code class='latex inline'>\displaystyle 5.00 \mathrm{~cm} </code></p>
<p>While flying, a helicopter pilot spots a water tower that is 4.8 km away to the north. At the same time, she also sees a monument that is 5.6 km away to the south. The tower and the monument are separated by a distance of 7.0 km along the flat ground. Find the angles at which the pilot is viewing the water tower and the monument, to the nearest degree.</p><img src="/qimages/5714" />
<p> <code class='latex inline'> A </code> kite is <code class='latex inline'> 32 \mathrm{~m} </code> above the ground. The angle the kite string makes with the ground is <code class='latex inline'> 39^{\circ} </code> . How long is the kite string, to the nearest metre?</p>
<p>Two ships, the Albacore and the Bonito, are 50 km apart. The Albacore is N45°W of the Bonito. The Albacore sights a distress flare at 55°E. The Bonito sights the distress flare at 550°W. How far is each ship from the distress flare?</p>
<p>A person on the ground is directly between two helicopters that are flying toward each other at the same altitude. The first helicopter is 2.0 km away from the observer, at an angle of elevation of 30°, while the second helicopter is 3.5 km away. Round answers to the nearest tenth of a kilometre, if necessary.</p><p>a) Draw a diagram and label the known information.</p><p>b) How far apart are the helicopters?</p><p>c) What is their altitude?</p>
<p>Peggy&#39;s Cove Lighthouse, in Nova Scotia, is possibly the most photographed lighthouse in the world. The observation deck is about <code class='latex inline'> 20 \mathrm{~m} </code> above sea level. From the observation deck, the angle of depression of a boat is <code class='latex inline'> 6^{\circ} </code> . How far is the boat from the lighthouse, to the nearest metre?</p>
<img src="/qimages/10078" /><p>What is the area of this triangle?</p><p>A. <code class='latex inline'>\displaystyle 28.5 \mathrm{~cm}^{2} </code></p><p>C. <code class='latex inline'>\displaystyle 2.0 \mathrm{~cm}^{2} </code></p><p>B. <code class='latex inline'>\displaystyle 27.0 \mathrm{~cm}^{2} </code></p><p>D. <code class='latex inline'>\displaystyle 9.0 \mathrm{~cm}^{2} </code></p>
<p>Ryan is in a police helicopter 400 m directly above a highway. When he looks west, the angle of depression to a car accident is 65°. When he looks east, the angle of depression to the approaching ambulance is 30°.</p> <ul> <li>The ambulance is travelling at 80 km/h. How long will it take the ambulance to reach the scene of the accident?</li> </ul>
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