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HW Word Problems for Trig.

1. Flagpole To calculate the height h of a flagpole, you move 22 feet from the base and record the angle of elevation to the top to be 65°. Find the flagpole's height to the nearest foot.

2. Water Slide The angle of elevation from the base to the top of a water slide is about 28°. The horizontal length of the slide is about 45 feet. Find the height h of the slide.

3. Distance You are standing near the Washington Monument which is 555 feet tall. The angle of elevation from your position to the top of the monument is 45°. How far are you from the monument?

4. Ski Lift A chair lift on a ski slope has an angle of elevation of 28° and covers a total distance of 4640 feet. To the nearest foot, what is the vertical height h covered by the chair lift?

5. Airplane Landing You are preparing to land an airplane. You are on a straight line approach path that forms a 3° vertical angle with the runway. What is the distance d along this approach path to your touchdown point when you are 500 feet above the ground? Round your answer to the nearest foot.

6. Extension Ladders You are using extension ladders to paint a chimney that is 33 feet tall. The length of an extension ladder ranges in one-foot increments from its minimum length to its maximum length. For safety, you should always use an angle of about 75.5° between the ground and the ladder.

a Your smallest extension ladder has a maximum length of 17 feet.

How high does this ladder safely reach on a vertical wall?

b. You place the base of the ladder 3 feet from the chimney.

How many feet long should the ladder be?

c. To reach the top of the chimney, you need a ladder that reaches 30 feet high.

How many feet long should the ladder be?

Use the picture below to answer questions 7-9

7. At 2 P.M., the shadow of a lighthouse is 19 feet long and the angle of elevation is 75°. Find the height of the lighthouse.

8. At 4 P.M., the angle of elevation of the sun is 40°. Find the length of the shadow cast by the lighthouse

9. At 6 P.M., will the length of the shadow be longer or shorter than it was at 4 P.M.? Explain.

10. Distance You are on the west side of the Washington Monument which is 555 feet tall. Your friend is on the opposite (east) side. The angle of elevation from your position to the top of the monument is 42°. The angle of elevation from your friend's position to the top of the monument is 65°. To the nearest foot, how far are you from your friend?

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