Practice and Problem-Solving Exercises

A Practice

Find the values of the six trigonometric functions for the angle in standard position determined by each point. See Problem 1.

7. ( − 2 , 3 ) open negative 2 comma 3 close
8. (5, 12)
9. ( 1 , − 5 ) open 1 comma negative 5 close
10. ( − 2 , − 2 ) open negative 2 comma negative 2 close
11. ( − 2 , √ 7 ) open negative 2 comma radical 7 close
12. You want to build a bicycle ramp that is 10 ft long and makes a 30 ° 30 degrees angle with the ground. What would be the height of the ramp? See Problem 2.

13. In Δ ABC , cap delta find each value as a fraction and as a decimal. Round to the nearest hundredth. See Problem 3.

    

    1. sin A
    2. sec A
    3. cot A
    4. csc B
    5. sec B
    6. tan B
14. In Δ GHI , ∠ H cap delta is a right angle, G H = 40 , g h equals 40 comma and cos G = 40 41 . cosine g equals , 40 over 41 . . Draw a diagram and find each value in fraction and in decimal form.
    1. sin G
    2. sin I
    3. cot G
    4. csc G
    5. cos I
    6. sec H

Find each length x. Round to the nearest tenth. See Problem 4.

15. 
16. 
17. 

18. Indirect Measurement In 1915, the tallest flagpole in the world stood in San Francisco.

    

    1. When the angle of elevation of the sun was 55 ° , 55 degrees comma the length of the shadow cast by this flagpole was 210 ft. Find the height of the flagpole to the nearest foot.
    2. What was the length of the shadow when the angle of elevation of the sun was 34 ° ? 34 degrees question mark
    3. What do you need to assume about the flagpole and the shadow to solve these problems. Explain why.

In Δ ABC , ∠ C cap delta is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. See Problem 5.

19. b = 5 , c = 10 b equals 5 comma c equals 10
20. a = 5 , b = 6 eh equals 5 comma b equals 6
21. b = 12 , c = 15 b equals 12 comma c equals 15
22. a = 8.1 , b = 6.2 eh equals 8.1 comma b equals 6.2
23. b = 4.3 , c = 9.1 b equals 4.3 comma c equals 9.1
24. a = 17 , c = 22 eh equals 17 comma c equals 22

25. Rocket Science An observer on the ground at point A watches a rocket ascend. The observer is 1200 ft from the launch point B. As the rocket rises, the distance d from the observer to the rocket increases. See Problem 6.

    1. Express m ∠ A m angle eh in terms of d.
    2. Find m ∠ A m angle eh if d = 1500 ft. d equals , 1500 , ft. Round your answer to the nearest degree.
    3. Find m ∠ A m angle eh if d = 2000 ft. d equals , 2000 , ft. Round your answer to the nearest degree.

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