Question

find the length of side ( x ) in simplest radical form with a rational denominator.

Explanation:

Step1: Identify trigonometric ratio

For the 30° angle, $\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{x}{1}$

Step2: Substitute $\tan(30^\circ)$ value

$\tan(30^\circ) = \frac{1}{\sqrt{3}}$, so $x = \frac{1}{\sqrt{3}}$

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{3}$:
$x = \frac{1 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} = \frac{\sqrt{3}}{3}$

Answer:

$\frac{\sqrt{3}}{3}$