Question

find the measure of x.
round to the nearest hundredth

Explanation:

Step1: Recall tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 12^{\circ}$, the opposite side is 4 and the adjacent side is $x$. So, $\tan(12^{\circ})=\frac{4}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{4}{\tan(12^{\circ})}$. Since $\tan(12^{\circ})\approx0.2126$, then $x=\frac{4}{0.2126}\approx18.81$.

Answer:

$18.81$