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

If AC= 5ft, AB=3ft, then we can know that BC²=AB²-AC²， BC=12ft. We draw an angle bisector AD of angle A, and draw a vertical line of AB at point D, that's segment DE. Because of ∠CAD=∠EAD, △CAD≌△EAD. That means CD=DE, AC=AE=5ft, so BE=AB-AE=13-5=8ft. If CD=xft=DE, BD=(12-x)ft. According to the Pythagorean theorem, DE²+BE²=BD²，we can create a equation.                 x²+8²=(12-x)²        x=10/3 ft                                                  Then, we use Pythagorean theorem again , AC²+CD²=AD²，and we can get the length of angle bisector of angle A.