566 CHAPTER 8 Applications of Trigonometric Functions 8.2 Assess Your Understanding 3. Approximate ° sin40 and ° s i n 8 0 . (pp. 405–406) 4. Approximate − sin 0.76. 1 Express the answer in degrees. (pp. 488–489) 1. The difference formula for the sine function is ( ) − = A B sin . (p. 514) 2. Solve = A sin 1 2 if π ≤ ≤ A 0 . (pp. 493–496) ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. In Problems 11–18, solve each triangle. 11. 458 958 5 a b A 12. a b C 408 4 458 13. 858 508 3 c a B 14. 308 1258 10 c a A Skill Building 15. 458 408 7 c a C 16. 58 108 5 b a C 17. 408 1008 2 c a A 18. 308 1008 6 c a C In Problems 19–26, solve each triangle. 19. = ° = ° = A B a 55 , 25 , 4 20. = ° = ° = A C a 50 , 20 , 3 21. = ° = ° = B C b 64 , 47 , 6 22. = ° = ° = A B c 70 , 60 , 4 23. = ° = ° = A C c 110 , 30 , 3 24. = ° = ° = B C b 10 , 100 , 2 25. = ° = ° = A B c 40 , 40 , 2 26. = ° = ° = B C a 20 , 70 , 1 In Problems 27–38, two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s). 27. = = = ° a b A 3, 2, 50 28. = = = ° b c B 4, 3, 40 29. = = = ° b c B 9, 4, 115 30. = = = ° a c A 2, 1, 120 31. = = = ° a b A 7, 14, 30 32. = = = ° b c B 2, 3, 40 33. = = = ° b c B 4, 6, 20 34. = = = ° a b A 3, 7, 70 35. = = = ° a c C 8, 3, 125 36. = = = ° b c B 4, 5, 95 37. = = = ° a c C 7, 3, 12 38. = = = ° b c B 4, 5, 40 8. True or False When two sides and an angle are given, at least one triangle can be formed. 9. True or False The Law of Sines can be used to solve triangles where three sides are known. 10. Triangles for which two sides and the angle opposite one of them are known (SSA) are referred to as the . 5. Multiple Choice If none of the angles of a triangle is a right angle, the triangle is called . (a) oblique (b) obtuse (c) acute (d) scalene 6. For a triangle with sides a, b, c and opposite angles A, B, C, the Law of Sines states that . 7. Multiple Choice If two angles of a triangle measure ° 48 and ° 93 , what is the measure of the third angle? (a) ° 132 (b) ° 77 (c) ° 42 (d) ° 39 Concepts and Vocabulary 39. Finding the Length of a Ski Lift Consult the figure on the right. To find the length of the span of a proposed ski lift from P to Q, a surveyor measures ∠DPQ to be ° 25 and then walks back a distance of 1000 feet to R and measures ∠PRQ to be ° 15 . What is the distance from P to Q ? 40. Finding the Height of a Mountain Use the figure in Problem 39 to find the height QD of the mountain. Applications and Extensions 1000 ft 158 P R D 258 Q 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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