SOLUTION: Apply the Angle-Bisector Theorem to the smallest angle of the right triangle whose sides are 1, 2, and the square root of 3. The side of length 1 is divided by the bisector into se

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Question 1154275: Apply the Angle-Bisector Theorem to the smallest angle of the right triangle whose sides are 1, 2, and the square root of 3. The side of length 1 is divided by the bisector into segments of what lengths? Using a calculator, check your answer for the tangent of a 15-degree angle.
Answer by greenestamps(13200) About Me  (Show Source):
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The two sides of the bisected angle have lengths 2 and sqrt(3); so the side of length 1 is divided into two parts in the ratio 2:sqrt(3).

For calculating the tangent of 15 degrees, the side opposite the 15 degree angle has length

sqrt%283%29%2F%282%2Bsqrt%283%29%29

Then, since the side adjacent to the 15 degree angle has length sqrt(3), the tangent of the 15 degree angle is

%28sqrt%283%29%2F%282%2Bsqrt%283%29%29%29%2Fsqrt%283%29 = 0.2679491924

Evaluating the tangent of 15 degrees directly yields the same value.