Question

find the length of side $x$ in simplest radical form with a rational denominator.
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Simplify $\sqrt{12}$

$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$

Step2: Identify trigonometric ratio

For the $30^\circ$ angle, $\tan(30^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2\sqrt{3}}{x}$

Step3: Solve for $x$

$\tan(30^\circ) = \frac{1}{\sqrt{3}}$, so $\frac{1}{\sqrt{3}} = \frac{2\sqrt{3}}{x}$. Cross multiply: $x = 2\sqrt{3} \times \sqrt{3}$

Step4: Simplify the expression

$x = 2 \times 3 = 6$

Answer:

$x = 6$