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.

EXAMPLE 5 Find leg lengths using an angle of elevation

SOLUTION

sin 26o=

opp. hyp. Write ratio for sine of 26o.

sin 26o x

=14 Substitute.

14 sin 26o = 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.

EXAMPLE 5 Find leg lengths using an angle of elevation

cos 26o=

adj. hyp. Write ratio for cosine of 26o.

cos 26o y

=14 Substitute.

14 cos 26o = y Multiply each side by 14.

12.6 y Use a calculator to simplify.

STEP 2 Find the length of the base.

ANSWER The length of the base is about 12.6 feet.

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

sin 60o =opp. hyp.

=3

20.08660

cos 60o =adj. hyp.

=21

0.5000=

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 60o angle.

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GUIDED PRACTICE for Examples 5 and 6

7. WHAT IF?

In Example 5, suppose the angle of elevation is 35o. What is the new height and base length of the ramp?

ANSWER about 8 feet, about 11.5 ft

8. Use a special right triangle to find the sine and cosine of a 30o angle.

ANSWER 1 2

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