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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.
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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 = 1830 0.6000
cos W = adj. to W hyp = WV
UW = 2430 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.
ANSWERYou 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 = 915 0.6
cos S = adj. to S hyp = ST
SR = 1215 0.8
SOLUTION
= 35
= 45
Find SR, use the Pythagorean TheoremST2 + 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 = RT
SR = 3034 0.8824
cos S = adj. to S hyp = ST
SR = 1634 0.4706
SOLUTIONFind SR, use the Pythagorean TheoremST2 + 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.