REAL-WORLD APPLICATIONS nole leans away from the sun at an angle of 7° the vertical, as shown in Figure 27. When the elevation of the sun is 55°, the pole casts a shadow 12 feet long on the level ground. How long is the to pole? Round the answer to the nearest tenth. 7° | 55° B 42 ft Figure 27 1. Figure 29 shows a satellite orbiting Earth. The satellite passes directly over two tracking stations A alnd B, which are 69 miles apart. When the satellite Is on one side of the two stations, the angles of elevation at A and B are measured to be 86.2° and 83.9°, respectively. How far is the satellite from station A and how high is the satellite above the ground? Round answers to the nearest whole mile 31. Am in Cartesiar fast frequency: 500 Hz, slow and vertical 500 33. Amplitude: 8, fast period: period: 10 slow frequency: 10 Hz 35. D(t)= 20 (0.9086)' coordinate in the pola 3. Determ cos (4nt), 31 second to plot the in the opp CHAPTER 10 is a distan Section 10.1 1. The altitude extends from any vertex to the opposite side or to the line containing the opposite side at a 90° angle. the known values are the side opposite the missing angle and another side and its opposite angle. sides and a non-included angle. polar axis negative then mo point 3 u 3. When negative 5. A triangle with two to an an given 7. B= 72°, a ~ 12.0, positive 9. y= 20°, b2 4.5, c 1.6 down t b~19.9 11. b 3.78 15. One triangle, a 50.3°, ß~ 16.7°, a ~ 26.7 17. Two triangles, y 54.3°, B2 90.7°, b 2 20.9 or y' 125.7°, 13. c 13.70 7. (-5 B' 19.3°, b' 2 6.9 b~9.9 or B'~ 18.3°, y'~ 118.7°, b' ~ 3.2 19. Two triangles, B 75.7°, y~ 61.3°, 13. ( 21. Two triangles, a - 143.2°, ß= 26.8°, a 2 17.3 or a'~ 16.8°, B' 2 153.2°, a' 8.3 19. r 23. No triangle possible 25. A - 47.8° or A' ~ 132.2° 27. 8.6 29. 370.9 31. 12.3 33. 12.2 35. 16.0 25. 37. 29.7° 39. x = 76.9°or x = 103.1° 41. 110.6° 43. A 39.4, C 47.6, BC - 20.7 45. 57.1 47. 42.0 29. 49. 430.2 51. 10.1 53. AD - 13.8 55. AB - 2.8 57. L 49.7, N ~ 56.1, LN 2 5.8 59. 51.4 feet 31. 37. 61. The distance from the satellite to station A is approximately 1,716 miles. The satellite is approximately 1,706 miles above the ground. 71. 24.1 ft 73. 19,056 ft² 75. 445,624 square miles 77. 8.65 ft2 41 63. 2.6 ft 65. 5.6 km 67. 371 ft 69. 5,936 ft 45 Section 10.2 1. Two sides and the angle opposite the missing side. 3. s is the semi-perimeter, which is half the perimeter of the triangle. 5. The Law of Cosines must be used for any oblique (non-right) 9. 34.7 triangle, 7. 11.3 11. 26.7 13. 257.4 15 sible 17. 95.5° 19. 26.9° 21. B 45.9°, 6.4 3. A 20.6°, B 38.4°, c 51.1 2 98.4° 27. 177.56 in? 29. 0.04 m² 39. 70.7° 49. 1.41 35. 29.1 37. 0.5 45. 9.3 47. 43.52 55. 48.98 57. 52° 6. 24.0 km 69. 2,371 miles