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Pre-Calculus Homework Solutions 209

# Pre-Calculus Homework Solutions 209 - Plan Use the Distance...

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Plan: Use the Distance Formula to find the measure of each side. Then use one of the trigonometric ratios to write an equation. Use the inverse to find m X . Solve: XY [7 ( 5)] 2 (0 0) 2 144 0 or 12 YZ (0 7) 2 ( 35 0) 2 49 35 84 or 2 21 XZ [0 ( 5)] 2 ( 35 0) 2 25 35 60 or 2 15 cos X X X Y Z cos X 2 12 15 or 6 15 X cos 1 6 15 KEYSTROKES: [COS 1 ] [ 2 ] 15 6 m X 49.79703411 The measure of X is about 49.8. Examine: Use the sine ratio to check the answer. sin X X YZ Y sin X 2 12 21 or 6 21 X sin 1 6 21 KEYSTROKES: [SIN 1 ] [ 2 ] 21 6 m X 49.79703411 The answer is correct. 55. sin35° C 2 B 0 20sin35° CB KEYSTROKES: 20 35 CB 11.5 cos35° ¬ A 2 C 0 20cos35° ¬ AC KEYSTROKES: 20 35 AC 16.4 The perimeter is about 20 11.5 16.4 or 47.9 inches. 56. sin x ° 2 3 4 6 x ° sin 1 2 3 4 6 KEYSTROKES: [SIN 1 ] 24 36 x 41.8 Let a represent the side of the smaller triangle opposite the angle of measure y . (2 a ) 2 24 2 ¬ 36 2 4 a 2 576 ¬ 1296 4 a 2 ¬ 720 a 2 ¬ 180 a ¬ 180 or 6 5 tan y ° 6 24 5 tan y ° 4 5 y ° tan 1 4 5 KEYSTROKES: [TAN 1 ] [ 2 ] 5 4 y 29.2 57. tan55° ¬ 1 x 2 12tan55° ¬ x KEYSTROKES: 12 55 x 17.1 sin47° x y y sin x 47° KEYSTROKES: 12 55 47 y 23.4 58. tan32° 2 x 4 x tan 24 32° KEYSTROKES: 24 32 x 38.4 cos32° y x x cos32° y KEYSTROKES: 24 32 32 y 32.6 59. Let d represent the distance between Alpha Centauri and the sun. tan0.00021
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