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EXAMPLE 5

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. EXAMPLE 5. Find leg lengths using an angle of elevation. SKATEBOARD RAMP. Find the height. STEP 1. sin 26 o. =. x. =.

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EXAMPLE 5

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  1. 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. EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP

  2. Find the height. STEP 1 sin26o = x = opp. hyp. sin26o 14 14 sin 26o = x 6.1 x ANSWER The height is about 6.1 feet. EXAMPLE 5 Find leg lengths using an angle of elevation SOLUTION Write ratio for sine of 26o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  3. cos26o = cos26o y = adj. hyp. 14 14 cos 26o = x 12.6 x ANSWER The length of the base is about 12.6 feet. EXAMPLE 5 Find leg lengths using an angle of elevation Find the length of the base. STEP 2 Write ratio for cosine of 26o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  4. 3 3 Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 60oangle. adj. hyp. opp. hyp. sin60o = 0.08660 = 2 1 cos60o = = 0.5000 = 2 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 60o angle. SOLUTION

  5. Find the height. STEP 1 sin35o = x = opp. hyp. sin35o 14 14 sin 35o = x 8 x ANSWER The height is about 8 feet. for Examples 5, and 6 GUIDED PRACTICE 7. WHAT IF? In Example 5, suppose the angle of elevation is 35o. What is the new height and base length of the ramp? SOLUTION Write ratio for sine of 35o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  6. cos35o = cos35o y = adj. hyp. 14 14 cos 35o = x 11.5 x ANSWER The base length is about 11.5 feet. for Examples 5, and 6 GUIDED PRACTICE Find the length of the base. STEP 2 Write ratio for cosine of 35o. Substitute. Multiply each side by 14. Use a calculator to simplify.

  7. 3 3 Use the 30o - 60o - 90o Triangle Theorem to draw a right triangle with side lengths of 1, and 2. Then set up sine and cosine ratios for the 30oangle. adj. hyp. opp. hyp. 1 sin30o = = 2 cos30o = = 2 for Examples 5, and 6 GUIDED PRACTICE 8. Use a special right triangle to find the sine and cosine of a 30o angle. SOLUTION

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