In a right triangle δabc, the length of leg ac = 5 ft and the hypotenuse ab = 13 ft. find: the median to side bc the length of the angle bisector of angle ∠a.

To make the problem easier, make an illustration of the problem description like the one shown in the attached picture. The median to side BC and the angle bisector of A is just the same, which is represented by the red line. The solution is as follows:

Let's solve for BC using the Pythagorean equation.
BC = √(13²) - (5²) = 12 ft

Then,
Median = Angle Bisector = √((12/2)² + 5²) = 7.81 ft