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4.8 Applications and Models Solve the right triangle. B B = ? = 90 – 34.2 = 55.8 c C a tan 34.2 a = 13.18 19.4 a 34.2 b = 19.4 19.4 A cos 34.2 c 23.46 h 40’ If the ladder is 40’ long and the angle of elevation is 42 , how high up is the fireman? 42 h sin 42 40 26.77 ft. At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 35, while the angle to the top is 53. Find the height, s, of the smokestack alone. s x tan 35 200 xs tan 53 200 53 x 35 200 ft. x 140.04 x s 265.41 265.41 -140.04 125.37 ft. Trigonometry and Bearings N N 80 W E S 35 S 35 E W E S N 80 W A ship leaves port at noon and heads due west at 20 knots (nautical miles per hour). At 2 P.M. , to avoid a storm, the ship changes course to N 54 W. Find the ship’s bearing and distance from the port of departure at 3 P.M.. Now find angle A. 11.76 tan A 16.18 40 D c b =11.76 20 nm 54 36 d = 16.18 B 11.82 N 78.18W 11.82 2(20) = 40 nm A Find c. c = 57.4 nm