1. EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = 18 30 0.6000 cos W = adj. to W hyp = WV UW = 24 30 0.8000 SOLUTION = 3 5 = 4 5

2. 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.

3. EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse SOLUTION sin 35 o = opp hyp Write ratio for sine of 35 o. sin 35 o = 11 x Substitute. x sin 35 o = 11 Multiply each side by x. x = 11. sin 35 o Divide each side by tan. 35 o x 11. 0.5736 Use a calculator to find tan. 35 o x 19.2 Simplify. ANSWER You will need a little more than 19 feet of cable.

4. 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. cos R = adj. to R hyp = RT SR = 9 15 0.6 cos S = adj. to S hyp = ST SR = 12 15 0.8 SOLUTION = 3 5 = 4 5 Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR 2 12 2 + 9 2 = SR 2 15 = SR

5. 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. cos R = adj. to R hyp = RT SR = 30 34 0.8824 cos S = adj. to S hyp = ST SR = 16 34 0.4706 SOLUTION Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR 2 16 2 + 30 2 = SR 2 34 = SR

6. GUIDED PRACTICE for Examples 2, and 3 5. SOLUTION cos35 o = adj hyp Write ratio for cosine of 35 o. cos 35 o = x 19.2 Substitute. 19.2 cos35 o = x multiply each side by 19.2 In Example 3, use the cosine ratio to find the length of the other leg of the triangle formed. x = 15.7 Simplify.