Answer:
7.81 ft
Explanation:
Let us name the median AZ.
First we need to find the length of leg CB. We can do that with the Pythagorean Theorem (leg² + leg²= hypotenuse²)
AC² + CB²= AB²
5² + a²= 13²
25 + a²= 169
25-25 + a²= 169 -25
a²= 144
square root of 144 is 12
a=12
a=CB
12=CB, or CB=12
CZ≅ZB (Definition of median)
CZ=6
Now for the Pythagorean Theorem again.
AC² + CZ²= AZ²
5² + 6²= b²
25 + 36= b²
61= b²
7.81=b
AZ=b
AZ=median
median=7.81