Question

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

Answer 1

Answer: the length of the angle bisector of angle ∠A is 6 ft

Step-by-step explanation:

The diagram of the right angle triangle ABC is shown in the attached photo

Looking at triangle ABC,

cos θ = adjacent side/hypotenuse side

cos θ = 5/13 = 0.3846

θ = 67.38 degrees

The bisector of an angle divides it into two equal halves. The bisector is represented by line AD.

θ/2 = 67.38/2 = 33.69 degrees

Therefore,

Cos 33.69 = 5/AD

AD × Cos 33.69 = 5

AD = 5/Cos 33.69 = 5/0.832

AD = 6 ft