Question

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

Explanation:

Step1: Identify trigonometric ratio

For the 30° angle, the side of length 8 is opposite, and $x$ is adjacent. Use tangent:
$\tan(30^\circ) = \frac{8}{x}$

Step2: Solve for $x$

Rearrange to isolate $x$:
$x = \frac{8}{\tan(30^\circ)}$

Step3: Substitute $\tan(30^\circ)$ value

Since $\tan(30^\circ) = \frac{1}{\sqrt{3}}$:
$x = \frac{8}{\frac{1}{\sqrt{3}}} = 8\sqrt{3}$

Answer:

$8\sqrt{3}$