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!
Since the trapezoid is isosceles, we can break it up like so.
And now you can use the Pythagorean theorm.
$8^2 + h^2 = (4\sqrt 5)^2$