554 CHAPTER 8 Applications of Trigonometric Functions 43. Geometry The hypotenuse of a right triangle is 5 inches. If one leg is 2 inches, find the degree measure of each angle. 44. Geometry The hypotenuse of a right triangle is 3 feet. If one leg is 1 foot, find the degree measure of each angle. 45. Geometry A right triangle has a hypotenuse of length 8 inches. If one angle is 35 ,° find the length of each leg. 46. Geometry A right triangle has a hypotenuse of length 10 centimeters. If one angle is 40 ,° find the length of each leg. 47. Geometry A right triangle contains a 25° angle. (a) If one leg is of length 5 inches, what is the length of the hypotenuse? (b) There are two answers. How is this possible? 48. Geometry A right triangle contains an angle of 8 π radian. (a) If one leg is of length 3 meters, what is the length of the hypotenuse? (b) There are two answers. How is this possible? 49. Finding the Width of a Gorge Find the distance from A to C across the gorge illustrated in the figure. 100 ft A C B 35° Applications and Extensions 4. True or False sin52 cos48 ° = ° 5. Multiple Choice The sum of the measures of the two acute angles in a right triangle is . (a) 45° (b) 90° (c) 180° (d) 360° 6. When you look up at an object, the acute angle measured from the horizontal to a line-of-sight observation of the object is called the . 7. True or False In a right triangle, if two sides are known, we can solve the triangle. 8. True or False In a right triangle, if we know the two acute angles, we can solve the triangle. Concepts and Vocabulary In Problems 19–28, find the exact value of each expression. Do not use a calculator. 19. sin38 cos52 ° − ° 20. tan12 cot78 ° − ° 21. cos10 sin80 ° ° 22. cos40 sin50 ° ° 23. 1 cos 20 cos 70 2 2 − ° − ° 24. 1 tan 5 csc 85 2 2 + ° − ° 25. tan20 cos70 cos20 ° − ° ° 26. cot40 sin50 sin40 ° − ° ° 27. cos35 sin55 sin35 cos55 ° ° + ° ° 28. sec35 csc55 tan35 cot55 ° ° − ° ° In Problems 29–42, use the right triangle shown below. Then, using the given information, solve the triangle. 29. b B 5, 20 ; = = ° find a, c, and A 30. b B 4, 10 ; = = ° find a, c, and A 31. a B 6, 40 ; = = ° find b, c, and A 32. a B 7, 50 ; = = ° find b, c, and A 33. b A 4, 10 ; = = ° find a, c, and B 34. b A 6, 20 ; = = ° find a, c, and B 35. a A 5, 25 ; = = ° find b, c, and B 36. a A 6, 40 ; = = ° find b, c, and B 37. c B 9, 20 ; = = ° find b, a, and A 38. c A 10, 40 ; = = ° find b, a, and B 39. a b 5, 3; = = find c, A, and B 40. a b 2, 8; = = find c, A, and B 41. a c 2, 5; = = find b, A, and B 42. b c 4, 6; = = find a, A, and B Skill Building In Problems 9–18, find the exact value of the six trigonometric functions of the angle θ in each figure. 9. 5 12 u 10. 3 4 u 11. 3 2 u 12. 3 3 u 13. 2 4 u 14. 3 4 u 15. 1 2 u 16. 2 u 3 17. 1 u 5 18. 2 u 5 c a b A B
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