# Calculating length of triangle sides in trapezium

My younger brother has this mathematical problem to solve, and he came to me for help. At first I thought I could solve it by simply applying the Pythagorean theorem, but there seems to be more to it.

He mentioned the Thales theorem, which I had to do some research on (it's been almost 7 years ago for me now), but I don't see how it would apply here.

this is a drawing of the problem

Any help or hints about the first step here would be greatly appreciated. Thanks in advance!

$$8^2 + h^2 = (4\sqrt 5)^2$$