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Advanced Trigonometry Review Practice Questions

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Updated on Oct 2, 2011

Read the following study guide for a concept review:

Advanced Trigonometry Review Study Guide

Practice Questions

1. A motorcycle has two 14-inch-long pistons, which meet at a 45° angle at the bottom. How far apart are the tops of the pistons?
2. Denise wants to put mulch on a triangular flower bed that measures 12 feet by 10 feet by 8 feet. If she wants the mulch to be 4 inches thick, how many cubic feet of mulch will she need?
3. Rebecca needs a triangle with sides that measure 5 inches, 6 inches, and 7 inches for a project. What is the smallest angle of this triangle?
4. The flagpole on top of a building is 25 feet tall. If the angle from the ground to the top of the pole is 55° and the angle to the bottom of the pole is. 51°, then how tall is the building (without counting the flagpole)?
5. A car is driven on a straight road for 25 miles. When the drive begins, a mountain in the distance is 30° to the right of the road. When the car stops after being driven the 25 miles, the mountain appears to be 45° to the right. How far away is the mountain from the car at this time?
6. Marissa tap dances 20 feet straight across a stage. She then turns 38° and taps 12 feet further. How far is she now from where she started?
7. A ship spots a lighthouse at 17° north of east, then sails 10° west of north for 15 miles. The lighthouse is then 2° south of east. How far is the ship from the lighthouse at this point?
8. June, standing 100 feet away from a church, sees the tip of the steeple to be about 51° above the horizontal. The base of the steeple appears to be 42° above the horizontal. How tall is the steeple of the church?
9. Two straight antenna meet at a 17° angle. If one is 40 inches long and the other is 50 inches long, how far apart are the tips of the antenna?
10. Suppose you want to adjust the antenna from the last problem so that their ends are 25 inches apart. At what angle should they be set?
11. What is the area of a regular heptagon (a seven-sided figure with all angles the same) with each side 8 inches in length?
12. An insect's wing is in the shape of a triangle, measuring 10 mm by 17 mm by 15 mm. What is the surface area of the wing?
13. Andy sees a mountain to the north. He then hikes straight northeast for 3.4 miles. At this point, the mountain now appears to be 23° west of north. How far away is the mountain?
14. Two children, Bailey and Maddie, are playing together. Just for fun, they run apart at a 120° angle. Bailey runs straight for 70 feet while Maddie runs straight for 55 feet. When they stop, how far apart are they?
15. A triangular plot of land measures 398 feet by 471 feet by 503 feet. How many acres is this? (Remember that an acre is 43,560 square feet.)
16. Todd stands on the ground and looks up at an office building. The angle to the first window is 42°. The angle to the window above it is 47°. Assuming that the first window is 10 feet below the second, how far away is the building?
17. A team of explorers is trying to map a series of islands. As a guide, they use the highest point on each island. From one point on a beach, the mountaintop of an adjacent island appears to be 27° above the horizontal. From a second point, 500 feet directly back, the angle is 25°. How far away is the mountain (measured horizontally) from the first point on the beach?
18. The end of a 20-foot ladder rests on a railing. The end of a 12-foot ladder is right next to it. Suppose the longer ladder touches the ground 10 feet further away than the shorter ladder. How tall is the railing?
19. Donald wants to cut a sail that is 17 feet by 12 feet by 8 feet. How many square feet of sailcloth will be needed? What will be the measure of the obtuse angle of the sail?
20. Heather wants to cover a triangle with gold leaf. The three sides of the triangle are 40 inches by 35 inches by 37 inches. How many square inches of gold leaf will she need?
21. Kelli has collected four triangles. The first is 4 inches by 6 inches by 7 inches. The second is 3 inches by 4 inches by 6 inches. The third is 8 inches by 10 inches by 13 inches. The last is 12 inches by 14 inches by 17 inches. Which of these triangles has the largest angle?
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