EXAMPLE 2 Find cosine ratios Find cos U

EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. SOLUTION cos U = adj. to U = hyp UV = UW 18 = 30 3 5 0. 6000 W cos W = adj. to = hyp WV = UW 24 = 30 4 5 0. 8000

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse DOG RUN You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse SOLUTION sin 35 o = opp hyp sin 35 o = 11 x Substitute. x sin 35 o = 11 Multiply each side by x. x = x x 11. sin 35 o 11. 0. 5736 19. 2 Write ratio for sine of 35 o. Divide each side by tan. 35 o Use a calculator to find tan. 35 o Simplify. ANSWER You will need a little more than 19 feet of cable.

GUIDED PRACTICE for Examples 2, and 3 In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary. SOLUTION Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR 2 122 + 92 = SR 2 15 = SR R cos R = adj. to = hyp RT SR = 9 15 = 3 5 0. 6 S cos S = adj. to = hyp ST SR = 12 15 = 4 5 0. 8

GUIDED PRACTICE for Examples 2, and 3 In Exercises 3 and 4, find cos R and cos S. Write each answer as a decimal. Round to four decimal places, if necessary. SOLUTION Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR 2 162 + 302 = SR 2 34 = SR R cos R = adj. to = hyp RT SR = 30 34 0. 8824 S cos S = adj. to = hyp ST SR = 16 34 0. 4706

GUIDED PRACTICE for Examples 2, and 3 In Example 3, use the cosine ratio to find the length of the other leg of the triangle formed. 5. SOLUTION cos 35 o = o cos 35 = 19. 2 cos 35 o = adj hyp x 19. 2 x x = 15. 7 Write ratio for cosine of 35 o. Substitute. multiply each side by 19. 2 Simplify.