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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!

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Since the trapezoid is isosceles, we can break it up like so.

enter image description here

And now you can use the Pythagorean theorm.

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

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  • $\begingroup$ Thank you very much! That was exactly what I was looking for. $\endgroup$ – Thrindil Feb 8 at 1:26

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