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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. STEP1 Because all 30o-60o-90o triangles are similar, you can simplify your calculations by choosing 1 as the length of the shorter leg. Use the 30o-60o-90o Triangle Theorem to find the length of the longer leg. EXAMPLE 4 Use a special right triangle to find a tangent Use a special right triangle to find the tangent of a 60o angle.

  4. longer leg = shorter leg 3 3 3 x x = = 1 EXAMPLE 4 Use a special right triangle to find a tangent 30o- 60o- 90oTriangle Theorem Substitute. Simplify.

  5. 3 3 3 tan60o = tan60o = 1 opp. adj. tan60o = ANSWER The tangent of any 60o angle is 1.7321 EXAMPLE 4 Use a special right triangle to find a tangent STEP2 Write ratio for tangent of 60o. Substitute. Simplify.

  6. 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.

  7. 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.

  8. 3 3 3 3 tan60o = opp. adj. 5 tan60o = 5 tan 60o = ANSWER The tangent of any 60o angle is for Examples 2, 3, and 4 GUIDED PRACTICE Find the value of x. Round to the nearest tenth. What If ?In Example 4, suppose the side length of the shorter leg is 5 instead of 1. Show that the tangent of 60° is still equal to 5. Write ratio for tangent of 60o. Substitute. Simplify.

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