Na 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.

First find the length of leg BC by using the Pythagorean theorem BC=132+52=12 ft if we find the midpoint of BC which is 6 ft we find where the angle bisector would touch the BC. From there we construct another triangle ANC where AC is equal to 5 ft and NC is equal to 6 ft where we can again use the Pythagorean theorem to find the length of the hypotenuse which is the angle bisector AN=Angle Bisector=62+52=7.8102 ft.