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Law of Sines and Cosines Analysis Name_________________ Date_________________ 1. An airplane A takes off from carrier B and flies in a straight line for 12 miles. At that instant, an observer on destroyer C located 5 miles from the carrier, notes that the angle determined by the carrier, the destroyer (vertex) and the plane is 37°. How far is the plane from the destroyer? 2. A 100-foot-tall antenna tower is to be placed on a hillside that makes an angle of 12° with the horizontal. It is to be anchored by tow cables from the top of the tower to points 85 feet uphill and 95 feet downhill from the base. How much cable is needed? 3. A plane flying in a straight line passes directly over a point A on the ground and later over a point B which is 3 miles from A. A few minutes later after the plane passes over B. the angle of elevation from A to the plane is 43° and the angle of elevation from B to the plane is 67°. How high is the plane at that moment? 4. Two trains leave a station on different tracks. The tracks make an angle of 125° with the station as vertex. The first train travels at an average speed of 100 miles per hour and the second travels at an average speed of 65 miles per hour. How for apart are the two trains after 2 hours? 5. A forest fire is spotted from two fire towers. The triangle determined by the two towers and the fire has angles of 28° and 37° at the tower vertices. If the towers are 3000 meters apart, which one is closer to the fire? Law of Sines/Cosines Page 2 Analysis 6. At Wrigley Field in Chicago, the straight-line distance from home plate over second base to the centerfield wall is 400 feet. How far is it from first base to the same point at the centerfield wall? 7. If a gallon of paint covers 400 square feet, how many gallons are needed to paint a triangular deck with sides of 65 feet, 72 feet, and 88 feet? 8. A boat runs in a straight line for 3 miles, and then it makes a 45° turn and goes for another 6 miles. How far is the boat from its starting point? 9. One diagonal of a parallelogram is 6 inches long and the other is 13 inches long. They form a 42° angle with each other. How long are the sides of a parallelogram? (Hint: the diagonals of a parallelogram bisect each other.) 10. Find the angles of a triangle whose vertices are (0,0), (5,-2), and (1,-3). Law of Sines/Cosines Analysis B Page 3 7.35 " C 20.62" A 8.04" 11. Assuming that the circles in the figure are mutually tangent, find the lengths of sides and the measures of the angles of triangle ABC.