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

= UVUW = 18

30 0.6000

cos W = adj. to W hyp

= WVUW = 24

30 0.8000

SOLUTION

= 35

= 45

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 35o =opp hyp Write ratio for sine of 35o.

sin 35o = 11x

Substitute.

x sin 35o = 11 Multiply each side by x.

x = 11. sin 35o Divide each side by tan. 35o

x 11. 0.5736

Use a calculator to find tan. 35o

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

= RTSR = 9

150.6

cos S = adj. to S hyp

= STSR = 12

15 0.8

SOLUTION

= 35

= 45

Find SR, use the Pythagorean Theorem

ST2 + TR2 = SR2

122 + 92 = SR2

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

= RTSR = 30

340.8824

cos S = adj. to S hyp

= STSR = 16

34 0.4706

SOLUTION

Find SR, use the Pythagorean Theorem

ST2 + TR2 = SR2

162 + 302 = SR2

34 = SR

GUIDED PRACTICE for Examples 2, and 3

5. SOLUTION

cos35o =adj hyp Write ratio for cosine of 35o.

cos 35o = x

19.2Substitute.

19.2 cos35o = 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.