7-10 642 CHAPTER 7 Applications of Trigonometry 35. Answer each question and justify your response using a diagram, but do not solve. 6.7 km 10.9 km a. 25. Given AABC with LA = (a) what length for side a will produce a right triangle? (b) How many triangles can be formed if side a = 8 cm? (c) If side a = 12 cm, how many triangles can be formed? (d) If side a = 25 cm, how many triangles can be formed? 30° and side c = 20 cm, 38° B AF 36. 398 mm = 6V3 m, 47. 465 mm 26. Given AABC with LA = 60° and side c = (a) what length for side a will produce a right triangle? (b) How many triangles can be formed if side a = 8 m? (c) If side a = 10 m, how many triangles can be formed? (d) If side a = 15 m, how many triangles can be formed? 59° as b. in of 37. As Solve using the law of sines and a scaled drawing. If two triangles exist, solve both completely. 2.6 x 1025 mi B bot ГOL that 28. side a = 36.5 yd ZB = 67° %3D 27. side b = 385 m ZB = 67° is al Clas 62° %3D %3D side b = 12.9 yd side a = 490 m Soru 30. side c = 10V3 in. ZA = 60° the c 29. side c = 25.8 mi ZA = 30° side a = 12.9 mi 38. B 6.8 X 1013 km separ side a = 15 in. a. %3D 48. Plane 31. side c = 58 mi ZC = 59° 32. side b = 24.9 km LB = 45° parall from with th %3D side a = 32.8 km side b = 67 mi b. as the indicat triangle, or two triangles can be formed from the diagrams given (diagrams may not be to scale), then solve. If two solutions exist, solve both completely. Note the arrowhead marks the side of undetermined length. Use the law of sines to determine if no triangle, one of Cirr applied to solve a triangle. Solve for the unknown angle (if possible), then determine if a second angle (0° < 0 < 180°) exists that also satisfies the proportion. For Exercises 39 to 44, assume the law of sines is being Assume both pla roughly that the sin B sin 60° 40. sin 48° sin A 39. 12 33. 32 0 is abou 27 Class M sin 65° sin B 42. 5.2 58 ft and Cirru sin C sin 57° 41. 4.9 determine 59° %3D 67 ft 35.6 40.2 sin 29° sin B 44. distances A alignment 49, Radar de sin 15° sin A 43. 280 121 321 34. 52 from a ma the port at shown. (a) a/432 cm maximum r ship's radar the departin detected? (b 38° b A- 382 cm maximum ra triple angle formula for sine is given here. Use the formula to find an exact value for sin 135°, then verify the result using a ship's radar far from port when it is fire > WORKING WITH FORMULAS 45. Triple angle formula for sine: sin(30) = 3 sin 0 - 4 sin'0 Most students are familiar with the double angle formula for sine: sin(20) = 2 sin 0 cos 0. The reference angle. %3D B. 2.9 X 1025 mi C) 59X 1013 km