That's great, but, just for educational purposes of our readers, there is a geometric method without the need for the trigonometry formulas.
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That's great, but, just for educational purposes of our readers, there is a geometric method without the need for the trigonometry formulas.
But we invented trigonometry (and algebra) so we didn't have to be clever about geometry any more! :)
I actually started out with a triangle dissection but I couldn't figure out the trick showing that you could pack exactly four triangles into the rectangle.
Now that I say that, it's probably something like using "all triangles with the same height and base have the same area" but I tend not to think in terms of non-rigid transformations.