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EXAMPLE 2

x. x. 17.6. tan 32 o. =. opp. adj. tan 32 o. 11. = 11. =. x. x =. x tan 32 o. 11. 11. tan 32 o. 0.6249. EXAMPLE 2. Find a leg length. Find the value of x. ALGEBRA. SOLUTION. Use the tangent of an acute angle to find a leg length. Write ratio for tangent of 32 o.

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EXAMPLE 2

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  1. x x 17.6 tan32o = opp. adj. tan32o 11 = 11 = x x = xtan 32o 11 11 tan32o 0.6249 EXAMPLE 2 Find a leg length Find the value of x. ALGEBRA SOLUTION Use the tangent of an acute angle to find a leg length. Write ratio for tangent of 32o. Substitute. Multiply each side by x. Divide each side by tan 32o Use a calculator to find tan 32o Simplify

  2. tan70o = h. tan70o = opp. adj. 40. 40 tan 70o = h 109.9 h ANSWER The lamppost is about 110 inches tall. EXAMPLE 3 Estimate height using tangent LAMPPOST Find the height hof the lamppost to the nearest inch. Write ratio for tangent of 70o. Substitute. Multiply each side by 40. Use a calculator to simplify.

  3. 22 = tan61o opp. adj. = x tan61o xtan 61o = 22 x 12.2 = for Examples 2, 3, and 4 GUIDED PRACTICE Find the value of x. Round to the nearest tenth. Write ratio for tangent of 60o. Substitute. Multiply each side by x. Simplify.

  4. x = tan56o opp. adj. = 13 tan56o 13 tan 56o = x x 19.3 = for Examples 2, 3, and 4 GUIDED PRACTICE Find the value of x. Round to the nearest tenth. Write ratio for tangent of 56o. Substitute. Multiply each side by 13. Simplify.

  5. 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.

  6. 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.

  7. Angle of elevation

  8. Angle of depression

  9. 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? EXAMPLE 4 Find a hypotenuse using an angle of depression SKIING

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