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Finding Length in Trigonometry Practice Questions

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Updated on Oct 2, 2011

Read the following study guide for a concept review:

Finding Length in Trigonometry Study Guide

Practice Questions

1. A 25-foot ladder leans against a wall. If it makes an angle of 72° with the ground, how high up the wall does it reach?
2. A 40-foot ladder leans against a tree. If the angle formed by the ladder and the ground measures 81°, how high up in the tree does the ladder reach?
3. A 30-foot ladder comes with instructions that say that it should never make more than a 75° angle with the ground. How far should the base of the ladder be kept from the base of a wall it is leaned against?
4. A 50-foot wire is pulled tight from the top of a pole to the ground. If it makes a 53° angle with the ground, how tall is the pole?
5. A wire will be attached from the top of a 20-foot telephone pole to the ground. If it should make a 60° angle with the ground, how long should the wire be?
6. A wire runs from the top of a radio tower to a point 25 feet from the base of the tower. If the wire makes an 81 ° angle with the ground, how tall is the tower?
7. A person at the top of a 100-foot tower sees a bear in the distance. If the bear appears to be 5° below the horizontal, how far is it from the base of the tower?
8. The pilot of an airplane sees a target at 15° below the horizontal. If the plane is 20,000 feet off the ground, how far away is the target (directly along the diagonal)?
9. The top of a tree appears to be 25° above the horizonal when viewed from 60 feet away. How tall is the tree?
10. A mountaintop appears 10° above the horizontal when a person views it from 5 miles away. How much higher is the mountain than where the person is standing?
11. A security camera is installed 20 feet from the wall of a museum. If the camera can rotate 40° to the left and 40° to the right, how many feet of wall can it observe?
12. A 6-foot-tall photographer wants to view a 50-foot-tall building so that it is no more than 35° from the horizontal. How far back should the photographer stand?
13. An airplane that is cruising at 30,000 feet appears to be 50° above the horizontal. How far away is the airplane (straight through the air)?
14. A hiker sees a stack of rocks directly across a river. After he walks 80 feet along the riverside, the rocks appear at a 35° angle (see Figure 13.7). How wide is the river?
  Figure 13.7
15. When the sun is 25° above the horizon, a tree casts a 40-foot shadow. How tall is the tree?
16. A person holds a laser pointer 3 feet off the ground. If it is aimed at 4° below horizontal, how far will the point of light be from where the person is standing?
17. A hot air balloon is 2,000 feet off the ground. The destination can be seen at 15° below the horizontal. How far away is the destination (measured along the ground)?
18. A 6-foot-Iong piece of wood leans against a wall. If it makes an angle of 15° with the wall, how far is the bottom of the board from the wall?
19. A ramp runs at a 20° angle up to a height of 5 feet. How long is the diagonal of the ramp?
20. A road descends from the top of a mountain at a 5° angle. If the road is 8 miles long to the bottom, how tall is the mountain?
21. A 50-foot rope is tied to a window. A person on the ground takes the end of the rope and walks until it is pulled straight. At this point, the rope makes a 37° angle with the ground. How high up is the window?
22. When the sun is 28° above the horizon, a tall rock mesa casts a shadow that is 400 feet long. How tall is the mesa?
23. A ramp must be built at a 14.5° angle to reach a point 4.2 feet off the ground. How long must the ramp be (along the ground)?
24. If a 10-foot pole is leaned against a wall at a 45° angle, how high up will it reach?
25. Two buildings, 100 feet apart, face each other. A person in one building looks up at a 58° angle (from the horizontal) to a person in the other building. What is the diagonal distance between them?
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