question\nfind the length of side $x$ in simplest radical form with a rational denominator.

Explanation:

Step1: Identify trigonometric ratio

For the $60^\circ$ angle, $\tan(60^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{9}$

Step2: Solve for $x$

$x = 9 \times \tan(60^\circ)$ Since $\tan(60^\circ) = \sqrt{3}$, substitute: $x = 9\sqrt{3}$

Answer:

$9\sqrt{3}$