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

Question

Skyler Morse

Mathematics

7 August, 03:28

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

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Davin · Answer 1

First, we have to find the measure of the angle A.

We will use the cos formula:

cos A = AC/AB = 5/13.

Then, using the inverse sin function (You can find on any scientific calculator) we get:

Measure A = sin^ (-1) (5/13) = 22°.

So the half the angle A measure A' = 22°/2 = 11°.

Then using the cos function again and denoting the length of the bisector as x, we have:

cos A' = 5/x then x = 5/cosA' = 5.

The length of the angle bisector of angle ∠A is 5 units.