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EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You need to find the height and length of the base of the ramp.

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EXAMPLE 5 Find leg lengths using an angle of elevation SOLUTION sin 26 o = opp. hyp. Write ratio for sine of 26 o. sin 26 o x = 14 Substitute. 14 sin 26 o = x Multiply each side by 14. 6.1 x Use a calculator to simplify. STEP 1 Find the height. ANSWER The height is about 6.1 feet.

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EXAMPLE 5 Find leg lengths using an angle of elevation cos 26 o = adj. hyp. Write ratio for cosine of 26 o. cos 26 o y = 14 Substitute. 14 cos 26 o = x Multiply each side by 14. 12.6 x Use a calculator to simplify. STEP 2 Find the length of the base. ANSWER The length of the base is about 12.6 feet.

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EXAMPLE 6 Use a special right triangle to find a sine and cosine Use a special right triangle to find the sine and cosine of a 60 o angle. SOLUTION Use the 30 o - 60 o - 90 o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 60 o angle. 3 sin 60 o = opp. hyp. = 3 2 0.08660 cos 60 o = adj. hyp. = 2 1 0.5000 =

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GUIDED PRACTICE for Examples 5, and 6 7.7. WHAT IF? In Example 5, suppose the angle of elevation is 35 o. What is the new height and base length of the ramp? SOLUTION sin 35 o = opp. hyp. Write ratio for sine of 35 o. sin 35 o x = 14 Substitute. 14 sin 35 o = x Multiply each side by 14. 8 x Use a calculator to simplify. STEP 1 Find the height. ANSWER The height is about 8 feet.

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GUIDED PRACTICE for Examples 5, and 6 cos 35 o = adj. hyp. Write ratio for cosine of 35 o. cos 35 o y = 14 Substitute. 14 cos 35 o = x Multiply each side by 14. 11.5 x Use a calculator to simplify. STEP 2 Find the length of the base. ANSWER The base length is about 11.5 feet.

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GUIDED PRACTICE 8. Use a special right triangle to find the sine and cosine of a 30 o angle. for Examples 5, and 6 SOLUTION Use the 30 o - 60 o - 90 o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 30 o angle. 3 sin 30 o = opp. hyp. = 2 1 cos 30 o = adj. hyp. = 2 3

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