## Geometry: Common Core (15th Edition)

$x = 5$ $y = 5 \sqrt 3$
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 measures $60^{\circ}$. 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: $10 = 2x$ Divide each side by $2$ to solve for $x$: $x = 5$ 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: $y = 5 \sqrt 3$