Question

find the measure of x. round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 12^{\circ}$, the opposite side to the angle 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 $x=\frac{4}{\tan(12^{\circ})}$. We know that $\tan(12^{\circ})\approx0.2126$. Then $x=\frac{4}{0.2126}\approx18.81$.

Answer:

$18.81$