785 8.1 The Law of Sines 68. Flight Path of a Plane A pilot flies her plane on a bearing of 35° 00′ from point X to point Y, which is 400 mi from X. Then she turns and flies on a bearing of 145° 00′ to point Z, which is 400 mi from her starting point X. What is the bearing of Z from X, and what is the distance YZ? 69. Distance to the Moon The moon is a relatively close celestial object, so its distance can be measured directly by taking two different photographs at precisely the same time from two different locations. The moon will have a different angle of elevation at each location. On April 29, 1976, at 11:35 a.m., the lunar angles of elevation during a partial solar eclipse at Bochum in upper Germany and at Donaueschingen in lower Germany were measured as 52.6997° and 52.7430°, respectively. The two cities are 398 km apart. Calculate the distance to the moon, to the nearest thousand kilometers, from Bochum on this day, and compare it with the actual value of 406,000 km. Disregard the curvature of Earth in this calculation. (Data from Scholosser, W., T. SchmidtKaler, and E. Milone, Challenges of Astronomy, Springer-Verlag.) 70. Ground Distances Measured by Aerial Photography The distance covered by an aerial photograph is determined by both the focal length of the camera and the tilt of the camera from the perpendicular to the ground. A camera lens with a 12-in. focal length will have an angular coverage of 60°. If an aerial photograph is taken with this camera tilted u = 35° at an altitude of 5000 ft, calculate to the nearest foot the ground distance d that will be shown in this photograph. (Data from Brooks, R., and D. Johannes, Phytoarchaeology, Dioscorides Press.) Find the area of each triangle using the formula = 1 2bh, and then verify that the formula = 1 2 absinC gives the same result. 71. C B A 608 2 1 3 72. C B A 608 608 2 2 2 3 73. A B C 458 2 1 2 74. A C B 458 1 2 2 d 358 608 Bochum Moon Donaueschingen NOT TO SCALE Find the area of each triangle ABC. See Examples 8 and 9. 75. A = 42.5°, b = 13.6m, c = 10.1m 76. C = 72.2°, b = 43.8 ft, a = 35.1 ft 77. B = 124.5°, a = 30.4 cm, c = 28.4 cm 78. C = 142.7°, a = 21.9km, b = 24.6km 79. A= 56.80°, b = 32.67 in., c = 52.89 in. 80. A = 34.97°, b = 35.29m, c = 28.67m 81. A= 30.50°, b = 13.00 cm, C= 112.60° 82. A = 59.80°, b = 15.00m, C = 53.10°
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