# 7.6 Apply to Sine and Cosine Ratios - Mr. Hubarth's Website

7.6 Apply to Sine and Cosine Ratios Hubarth Geometry SOH - Sin = CAH - Cos = Sine and Cosine Ratios Let be a right triangle with acute angle A. The sine of angle A and the cosine of angle A (written sin A and cos A) are defined as follows: B hypotenuse sin A = cos A = leg opposite A C leg adjacent to A A Ex 1 Find Sine Ratios Find sin S and sin R. Write each answer as a fraction and as a decimal rounded to four places.

sin S sin R = opp. hyp = RT SR = 63 65 0.9692 = opp. hyp = ST SR

= 16 65 0.2462 Ex 2 Find Cosine Ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. hyp = UV UW = 18 30 = 3 5

cos W = adj. hyp = WV UW = 24 30 = 4 5 = 0.60 = 0.8000 Ex 3 Find a Hypotenuse Using an Angle of Depression You are skiing on a mountain with an altitude of 1200 feet. The angle of depression is 21o. About how far do you ski down the mountain? sin 21o

sin 21 x sin 21o o opp. hyp. = 1200 = x = 1200 x = 1200 sin 21o x 1200 0.3584 x 3348.2 Ex 4 Find Leg Lengths Using an Angle of Elevation

You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26. You need to find the height and length of the base of the ramp. sin 26o = sin 26o = 14 sin 26o 6.1 x opp. hyp. x 14 = x cos 26o = cos 26o = height is 6.1 ft

14 cos 26o 12.6 adj. hyp. y 14 = y y length is 12.6 ft Practice Find sin X and sin Y. Write each answer as a fraction and as a decimal. sin X = sin Y = sin X = sin Y = In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. 34 15 cos R = 0.6 cos S = 0.8 cos R = 0.88 cos S = 0.47

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