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.

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Presentation transcript:

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 = cos W = adj. to W hyp = WV UW = SOLUTION = 3 5 = 4 5

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 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 Use a calculator to find tan. 35 o x 19.2 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. cos R = adj. to R hyp = RT SR = cos S = adj. to S hyp = ST SR = SOLUTION = 3 5 = 4 5 Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR = SR 2 15 = SR

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 = cos S = adj. to S hyp = ST SR = SOLUTION Find SR, use the Pythagorean Theorem ST 2 + TR 2 = SR = SR 2 34 = SR

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 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.