EXAMPLE 5 Find leg lengths using an angle

EXAMPLE 5 Find leg lengths using an angle of elevation STEP 2 Find the

EXAMPLE 6 Use a special right triangle to find a sine and cosine Use

GUIDED PRACTICE 7. for Examples 5, and 6 WHAT IF? In Example 5, suppose

GUIDED PRACTICE for Examples 5, and 6 STEP 2 Find the length of the

for Examples 5, and 6 GUIDED PRACTICE 8. Use a special right triangle to

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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.

EXAMPLE 5 Find leg lengths using an angle of elevation SOLUTION STEP 1 Find the height. opp. sin 26 o = hyp. sin 26 o = x 14 Substitute. 14 sin 26 o = x 6. 1 Write ratio for sine of 26 o. x Multiply each side by 14. Use a calculator to simplify. ANSWER The height is about 6. 1 feet.

EXAMPLE 5 Find leg lengths using an angle of elevation STEP 2 Find the length of the base. adj. cos 26 o = hyp. cos 26 o = y 14 Substitute. 14 cos 26 o = x 12. 6 Write ratio for cosine of 26 o. x Multiply each side by 14. Use a calculator to simplify. 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 60 o angle. SOLUTION Use the 30 o - 60 o - 90 o Triangle Theorem to draw a right triangle with side lengths of 1, 3 and 2. Then set up sine and cosine ratios for the 60 o angle. o sin 60 opp. = = hyp. 3 2 adj. = hyp. 1 2 cos 60 o = 0. 08660 = 0. 5000

GUIDED PRACTICE 7. for Examples 5, and 6 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 STEP 1 Find the height. opp. sin 35 o = hyp. sin 35 o = x 14 14 sin 35 o = x 8 ANSWER x The height is about 8 feet. Write ratio for sine of 35 o. Substitute. Multiply each side by 14. Use a calculator to simplify.

GUIDED PRACTICE for Examples 5, and 6 STEP 2 Find the length of the base. adj. cos 35 o = hyp. cos 35 o = y 14 Substitute. 14 cos 35 o = x 11. 5 Write ratio for cosine of 35 o. x Multiply each side by 14. Use a calculator to simplify. ANSWER The base length is about 11. 5 feet.

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