Question

In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: b The length of the angle bisector of angle ∠A.

Answer 1

b = (5/3)√13

Explanation:

The cosine of ∠A is AC/AB = 5/13.

The cosine of half of ∠A is given by the half-angle formula ...

cos(A/2) = √((1 +cos(A))/2) = √((1 + 5/13)/2) = √(9/13) = 3/√13

The length of the segment b is found from ...

cos(A/2) = 5/b . . . . . adjacent side/hypotenuse

b = 5/cos(A/2) = 5/(3/√13)

b = (5/3)√13