Answer
$x = 6\sqrt 3$
$y = 12$
Work Step by Step
The diagram is that of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle because one angle measures $30^{\circ}$, another measures $90^{\circ}$, and the last angle must measure $60^{\circ}$.
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 $x$, the length of the longer leg:
$x = \sqrt 3(6)$
Rewrite the radical in a more standard form:
$x = 6\sqrt 3$
In this type of right triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for $y$, the length of the hypotenuse:
$y = 2(6)$
Multiply to solve for $y$:
$y = 12$
