In a right triangle ABC, the length of leg AC=5 ft and the hypotenuse AB=13 ft. Find: a. The median to side BC b. The length of the angle bisector of angle a

a. 6 feet

b. The length of the angle bisector of angle A is approximately 7.81 feet

Step-by-step explanation:

a. The given parameters of the right triangle ABC are;

The length of the leg AC = 5 ft.

The length of the hypotenuse AB = 13 ft.

Therefore, the length of the side BC = √((AB)² - (AC)²) = √((13 ft.²) - (5 ft.²)) = 12 ft.

The length to the middle of the side BC = BC/2 = (12 ft.)/2 = 6 ft.

b. The length of the angle bisector of angle A = The the length of the median from A to the side BC = √((BC)/2)² + (AC)²)

BC = √(((12 ft.)/2)² + (5 ft.)²) = √61 ft. ≈ 7.81 ft.