A 45-45-90 right triangle is isosceles. That means both legs are the same length, and its hypotenuse is √2 times the leg length. You can figure these facts using trigonometry or the Pythagorean theorem, or you can rely on your memory of them.
w = 8 . . . . . . . . . . . same as the leg length shown
x = y = 8√2 . . . . . hypotenuse of smaller triangle; both legs are the same
z = (8√2)√2 = 16 . . . . hypotenuse of larger triangle
