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Twenty Questions

Practice analytic geometry through real-life scenarios involving angles, distances, and heights. Solve ramp, pyramid, eagle, and flagpole problems to master unit 2 concepts.

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Twenty Questions

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  1. Twenty Questions Subject: Analytic Geometry Unit 2

  2. Twenty Questions

  3. Jessie is building a ramp loading motorcycles onto a trailer. The trailer is 2.8 ft off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15°. To the nearest hundredth of a foot, find the length of the ramp. • 10.8 ft.

  4. The largest Egyptian pyramid is 146.5 m high. When Ron stands far away from the pyramid, his angle of elevation is 20°. What is the horizontal distance between the center of the pyramid and Ron. Round to the nearest meter • 402 meters.

  5. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°. What is the horizontal distance between the eagle and its prey? Round to the nearest foot. • 1120 ft

  6. The coordinates of the vertices of triangle RPQ are R(2,-1) P(2,2) and Q(-2,-1). Find m∠P • 53°

  7. Find GH. Round to the nearest hundredth • 22.46 in

  8. The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV is 4:3. What are the width and height of a 27” TV screen? • Width 21.6 in height 16.2 in

  9. Write the trigonometric ratio for cos X as a fraction. • Cos x = 4/5

  10. The longest side of a 30°-60°-90° triangle measures 8. What is the length of the longer leg?

  11. When the angle of elevation of the sun is 50°, a flagpole casts a shadow that is 16.8 ft long. What is the height of the flagpole to the nearest foot?. • 20 ft

  12. A utility worker is installing a 25 ft telephone pole. The work order indicates that two guy wires (a wire running from the ground to the top of the pole) should be placed opposite each other and at a 65° angle of elevation to the pole. To the nearest tenth of a foot, how far apart are the guy wires? • 23.3 ft

  13. Find sin B as a decimal rounded to the nearest hundredth. • 0.55

  14. To the nearest tenth, what is the altitude of an equilateral triangle whose sides measures 43 cm? • 37.2 cm

  15. A 39-foot ladder is propped up against a wall so that it reaches 30 feet up the wall. What is the angle of elevation the ladder forms with the floor. • 50°

  16. Lindsey is 9.2 meters up, and the angle of depression from Lindsey to Pete is 79°. Find the distance from Pete to the base of the building to the nearest tenth of a meter. • 1.8 meters

  17. Lisa walks 15 feet from the base of the tree. She measures an angle of elevation from the ground to the nest 62°. Find how high the nest is above the ground, to the nearest foot. • 28 ft

  18. Find BD • 12.46 m

  19. Find QP • 19.70 mm

  20. Find ∠D. • 65°

  21. Find the length of GH • 7.64 ft

  22. A ramp is used to load a 4-wheeler onto a truck bed that is 3 ft above the ground. The angle that the ramp makes with the ground is 32°. What is the horizontal distance covered by the ramp? Round to the nearest hundredth. • 4.80 ft

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