Answer
$w =18$
$x =18\sqrt 3$
$y =18$
$z=18\sqrt 2$
Work Step by Step
1. Use the figure given in the exercise, we have $w=36sin30^\circ=18$
2. Use Pythagorean's Theorem, we have $x^2+w^2=36^2$, thus $x^2=36^2-18^2=972$ and $x=18\sqrt 3$ (or $x=36cos30^\circ=18\sqrt 3$ )
3. In the right triangle with $45^\circ$ angle, we have $y=w=18$
4. Use Pythagorean's Theorem, we have $z^2=w^2+y^2=2\cdot 18^2$ and $z=18\sqrt 2$ (or $z=\frac{w}{sin45^\circ}=18\sqrt 2$ )
