Since the assignment of labels to the vertices of the triangle is completely arbitrary, we can assume without loss of generality that angle C is the right angle. Since , we can say that .
We also know that since the two acute angles of a right triangle are complementary, (because ) and vice versa. Hence we can say that
So
But since the Pythagorean Identity gives us
John
My calculator said it, I believe it, that settles it
