795 8.2 The Law of Cosines 15. A 10 10 12 B C 16. A 8 10 4 B C 17. 558 A B C 100 90 18. A 9 7 5 B C Solve each triangle. See Examples 2 and 3. 19. A = 41.4°, b = 2.78yd, c = 3.92yd 20. C = 28.3°, b = 5.71 in., a = 4.21 in. 21. C = 45.6°, b = 8.94m, a = 7.23m 22. A = 67.3°, b = 37.9km, c = 40.8km 23. a = 9.3 cm, b = 5.7 cm, c = 8.2 cm 24. a = 28 ft, b = 47 ft, c = 58 ft 25. a = 42.9m, b = 37.6m, c = 62.7m 26. a = 189yd, b = 214yd, c = 325yd 27. a = 965 ft, b = 876 ft, c = 1240 ft 28. a = 324m, b = 421m, c = 298m 29. A = 80° 40′, b = 143 cm, c = 89.6 cm 30. C = 72° 40′, a = 327 ft, b = 251 ft 31. B = 74.8°, a = 8.92 in., c = 6.43 in. 32. C = 59.7°, a = 3.73mi, b = 4.70mi 33. A = 112.8°, b = 6.28m, c = 12.2m 34. B = 168.2°, a = 15.1 cm, c = 19.2 cm 35. a = 3.0 ft, b = 5.0 ft, c = 6.0 ft 36. a = 4.0 ft, b = 5.0 ft, c = 8.0 ft Concept Check Answer each question. 37. If we attempt to find any angle of a triangle with the values a = 3, b = 4, and c = 10 using the law of cosines, what happens? 38. “The shortest distance between two points is a straight line.” How is this statement related to the geometric property that states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side? Solve each problem. See Examples 1–4. 39. Distance across a River Points A and B are on opposite sides of False River. From a third point, C, the angle between the lines of sight to A and B is 46.3°. If AC is 350 m long and BC is 286 m long, find AB.
RkJQdWJsaXNoZXIy NjM5ODQ=