Answer
$x = 6 \sqrt 3$
Work Step by Step
In a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the hypotenuse is two times the shorter leg. Let's write an equation to solve for the length of the shorter leg:
$12 = 2$(shorter leg)
Divide each side by $2$ to solve for the shorter leg:
shorter leg = $6$
We don't want the length of the shorter leg; we want the length of the longer leg.
In a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the longer leg is $\sqrt 3$ times the shorter leg. Let's write an equation to solve for the length of the longer leg:
$x = \sqrt 3(6)$
Let's rewrite this:
$x = 6 \sqrt 3$
