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Use the tangent of an acute angle to find a leg length.
EXAMPLE 2 Find a leg length ALGEBRA Find the value of x. SOLUTION Use the tangent of an acute angle to find a leg length. tan 32o = opp. adj. Write ratio for tangent of 32o. tan 32o 11 = x Substitute. x tan 32o = 11 Multiply each side by x. x = 11 tan 32o Divide each side by tan 32o x 11 0.6249 Use a calculator to find tan 32o x 17.6 Simplify
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Estimate height using tangent
EXAMPLE 3 Estimate height using tangent LAMPPOST Find the height h of the lamppost to the nearest inch. tan 70o = opp. adj. Write ratio for tangent of 70o. tan 70o h. = 40. Substitute. Multiply each side by 40. 40 tan 70o = h Use a calculator to simplify. 109.9 h ANSWER The lamppost is about 110 inches tall.
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Find the value of x. Round to the nearest tenth.
GUIDED PRACTICE for Examples 2, 3, and 4 Find the value of x. Round to the nearest tenth. tan 61o = opp. adj. Write ratio for tangent of 60o. tan 61o 22 = x Substitute. x tan 61o = 22 Multiply each side by x. x 12.2 = Simplify.
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Find the value of x. Round to the nearest tenth.
GUIDED PRACTICE for Examples 2, 3, and 4 Find the value of x. Round to the nearest tenth. tan 56o = opp. adj. Write ratio for tangent of 56o. tan 56o x = 13 Substitute. 13 tan 56o = x Multiply each side by 13. 19.3 x = Simplify.
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Find leg lengths using an angle of elevation
EXAMPLE 5 Find leg lengths using an angle of elevation SOLUTION STEP 1 Find the height. 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. ANSWER The height is about 6.1 feet.
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Find leg lengths using an angle of elevation
EXAMPLE 5 Find leg lengths using an angle of elevation STEP 2 Find the length of the base. cos 26o = adj. hyp. Write ratio for cosine of 26o. cos 26o y = 14 Substitute. 14 cos 26o = x Multiply each side by 14. 12.6 x Use a calculator to simplify. ANSWER The length of the base is about 12.6 feet.
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Angle of elevation
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Angle of depression
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EXAMPLE 4 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 21o. About how far do you ski down the mountain?
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