797 8.2 The Law of Cosines 48. Distance between a Ship and a Submarine From an airplane flying over the ocean, the angle of depression to a submarine lying under the surface is 24° 10′. At the same moment, the angle of depression from the airplane to a battleship is 17° 30′. See the figure. The distance from the airplane to the battleship is 5120 ft. Find the distance between the battleship and the submarine. (Assume the airplane, submarine, and battleship are in a vertical plane.) Submarine 248 109 5120 ft 178 309 Battleship 49. Truss Construction A triangular truss is shown in the figure. Find angle u. 50. Truss Construction Find angle b in the truss shown in the figure. 51. Distance between a Beam and Cables A weight is supported by cables attached to both ends of a balance beam, as shown in the figure. What angles are formed between the beam and the cables? 52. Distance between Points on a Crane A crane with a counterweight is shown in the figure. Find the horizontal distance between points A and B to the nearest foot. 53. Distance on a Baseball Diamond A baseball diamond is a square, 90.0 ft on a side, with home plate and the three bases as vertices. The pitcher’s position is 60.5 ft from home plate. Find the distance from the pitcher’s position to each of the bases. 3rd base Home plate 1st base 90.0 ft 2nd base 60.5 ft 54. Distance on a Softball Diamond A softball diamond is a square, 60.0 ft on a side, with home plate and the three bases as vertices. The pitcher’s position is 46.0 ft from home plate. Find the distance from the pitcher’s position to each of the bases. 3rd base Home plate 1st base 60.0 ft 2nd base 46.0 ft u b 20 ft 16 ft 13 ft 90 ft ? ? 45 ft 60 ft 10 ft 10 ft C A B 1288
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