798 CHAPTER 8 Applications of Trigonometry 55. Distance between a Ship and a Point Starting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A. 56. Distance between Two Factories Two factories blow their whistles at exactly 5:00. A man hears the two blasts at 3 sec and 6 sec after 5:00, respectively. The angle between his lines of sight to the two factories is 42.2°. If sound travels 344 m per sec, how far apart are the factories? 57. Measurement Using Triangulation Surveyors are often confronted with obstacles, such as trees, when measuring. One technique used to obtain an accurate measurement is the triangulation method. A triangle is constructed around the obstacle, and one angle and two sides of the triangle are measured. Use this technique to find the length of the property line (the straight line between the two markers) shown in the figure. (Data from Kavanagh, B., Surveying Principles and Applications, Sixth Edition, Prentice-Hall.) 58. Path of a Ship A ship sailing due east in the North Atlantic has been warned to change course to avoid icebergs. The captain turns and sails on a bearing of 62°, then changes course again to a bearing of 115° until the ship reaches its original course. See the figure. How much farther did the ship have to travel to avoid the icebergs? Icebergs 50 mi E 59. Length of a Tunnel To measure the distance through a mountain for a proposed tunnel, a point C is chosen that can be reached from each end of the tunnel. See the figure. If AC = 3800 m, BC = 2900 m, and angle C = 110°, find the length of the tunnel. 60. Distance between an Airplane and a Mountain A person in a plane flying straight north observes a mountain at a bearing of 24.1°. At that time, the plane is 7.92 km from the mountain. A short time later, the bearing to the mountain becomes 32.7°. How far is the airplane from the mountain when the second bearing is taken? Find the measure of each angle u to two decimal places. 61. (6, 8) (4, 3) u x 0 y 62. (8, 6) (12, 5) x 0 u y 14.0 ft 13.0 ft 70.08 NOT TO SCALE Marker Marker 18.0 ft 14.0 ft A B 110° 2900 m 3800 m C Tunnel
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