In a $30^{\circ}$-$60^{\circ}$-$90^{\circ}$ right triangle, the side opposite the $60^{\circ}$ angle has length $5\sqrt{3}$. What is the length of the **hypotenuse**?

In a $30$-$60$-$90$ triangle, sides opposite $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$ are in ratio $1 : \sqrt{3} : 2$. Let the short leg (opposite $30^{\circ}$) be $x$. Then: - side opposite $60^{\circ} = x\sqrt{3} = 5\sqrt{3} \Rightarrow x = 5$. - hypotenuse $= 2x = 10$. - Trap A ($5$) is the short leg, not the hypotenuse. - Trap C ($5\sqrt{3}$) restates the given side. - Trap D ($10\sqrt{3}$) doubles the wrong side. Load-bearing relation: the hypotenuse equals **twice** the short leg in a $30$-$60$-$90$ triangle.