In a 45° - 45° - 90° right triangle, the length of the hypotenuse is #15sqrt2#, what is the length on one of the legs?
Call a the side and c the hypotenuse
Use the right triangle rule: a^2 + a^2 = c^2
2a^2 = 2(225) = 450 -> a^2 = 225 -> a = 15.
This is an isosceles right triangle, in which both legs have the same length. In an isosceles right triangle, the hypotenuse is
We can prove this with the Pythagorean theorem.