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

7.81 ft

Step-by-step 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