9 5 Trigonometric Ratios Vocabulary Trigonometric Ratio the
9. 5: Trigonometric Ratios
Vocabulary • Trigonometric Ratio: the ratio of the lengths of two sides of a right triangle • Angle of elevation: the angle that your line of sight makes with a line drawn horizontally.
Trigonometric Ratios • sine A = side opposite hypotenuse • cosine A = side adjacent hypotenuse • tangent A = side opposite side adjacent o p p o s it e hy po te nu se A adjacent
Example 1: Compare the sine, the cosine and the tangent ratios for A in each triangle below. sin A = 5/13 sin A =. 3846 tan A = 2. 5/6 cos A = 12/13 tan A =. 4167 cos A =. 9231 13 tan A = 5/12 5 tan A =. 4167 6. 5 2. 5 A A 12 6 sin A = 2. 5/6. 5 cos A = 6/6. 5 sin A =. 3846 cos A =. 9231
Example 2: Find the sine, cosine, and the tangent of the indicated angle E 14 a) E sin E = 48/50 = 0. 96 cos E = 14/50 =0. 28 tan E = 48/14 50 F = 3. 4286 D 48 b) D sin D = 14/50 = 0. 28 cos D = 48/50 =0. 96 tan D = 14/48 = 0. 2917
Example 3: Find the sine, the cosine, and the tangent of A √ 2 18 18 18 A sin A = 18/18√ 2 = 0. 7071 cos A = 18/18√ 2 = 0. 7071 tan A = 18/18 =1
Example 4: Find the sine, the cosine, and the tangent of A 10 5 A 5√ 3 sin A = 5/10 = 0. 5 cos A = 5√ 3/10 = 0. 8660 tan A = 5/5√ 3 = 0. 5774
Example 5: Use a calculator to approximate the sine, the cosine, and the tangent of 82. • sin 82 = 0. 9903 • cos 82 = 0. 1392 • tan 82 = 7. 1154
Example 6: You are measuring the height of a building. You stand 100 ft from the base of the building. You measure the angle of elevation from a point on the ground to the top of the building to be 48. Estimate the height of the building. 100(tan 48) = h 100(1. 1106) = h h 111 ft = h The building is about 111 ft tall 48 100 ft
Example 7: A driveway rises 12 feet over a distance d at an angle of 3. 5. Estimate the length of the driveway. d 12 d(sin 3. 5) =12 0. 0610 d= 12 d = 196. 7213 d = 197 ft
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