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

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) (Show Source): You can put this solution on YOUR website!

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

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

= 0.2679491924

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

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