Answer
$x = 20$
$y = 20 \sqrt 3$
Work Step by Step
The diagram is that of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle because one angle measures $30^{\circ}$ and another measures $90^{\circ}$, so the last angle must be $60^{\circ}$. In this type of right triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for $x$, the length of the shorter leg:
$40 = 2x$
Divide each side by $2$ to solve for $x$:
$x = 20$
In this triangle, the longer leg is $\sqrt 3$ times the length of the shorter leg. Let's set up that equation to solve for $y$, the length of the longer leg:
$y = 20 \sqrt 3$
