WarmUp 4 Exercises EXAMPLE Find a hypotenuse using

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Warm-Up 4 Exercises EXAMPLE Find a hypotenuse using an angle of depression SKIING You

Warm-Up 4 Exercises EXAMPLE Find a hypotenuse using an angle of depression SKIING You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21 o. About how far do you ski down the mountain?

Warm-Up 4 Exercises EXAMPLE Find a hypotenuse using an angle of depression SOLUTION sin

Warm-Up 4 Exercises EXAMPLE Find a hypotenuse using an angle of depression SOLUTION sin 21 = opp. hyp. Write ratio for sine of 21 o. sin 21 o = 1200 x Substitute. x sin 21 o = 1200 Multiply each side by x. x = 1200 sin 21 o Divide each side by sin 21 o x 1200 0. 3584 Use a calculator to find sin 21 o x 3348. 2 Simplify. o ANSWER You ski about 3348 meters down the mountain.

Warm-Up Exercises GUIDED PRACTICE 6. for Example 4 WHAT IF? Suppose the angle of

Warm-Up Exercises GUIDED PRACTICE 6. for Example 4 WHAT IF? Suppose the angle of depression in Example 4 is 28°. About how far would you ski?

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation SKATEBOARD RAMP

Warm-Up 5 Exercises EXAMPLE 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.

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation SOLUTION STEP

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

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation STEP 2

Warm-Up 5 Exercises EXAMPLE Find leg lengths using an angle of elevation STEP 2 Find the length of the base. adj. cos 26 o = hyp. y 14 cos 26 o = y 12. 6 ANSWER y Write ratio for cosine of 26 o. Substitute. Multiply each side by 14. Use a calculator to simplify. The length of the base is about 12. 6 feet.

Warm-Up 6 Exercises EXAMPLE Use a special right triangle to find a sine and

Warm-Up 6 Exercises EXAMPLE 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

Warm-Up Exercises GUIDED PRACTICE for Examples 5 and 6 7. WHAT IF? In Example

Warm-Up Exercises GUIDED PRACTICE for Examples 5 and 6 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? 8. Use a special right triangle to find the sine and cosine of a 30 o angle.

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