Question

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

Explanation:

Step1: Use the tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 52^{\circ}$, the opposite side is $x$, and the adjacent side is $12$. So, $\tan(52^{\circ})=\frac{x}{12}$.

Step2: Solve for $x$

Multiply both sides of the equation by $12$: $x = 12\times\tan(52^{\circ})$.
We know that $\tan(52^{\circ})\approx1.2799$. Then $x=12\times1.2799$.
$x = 15.3588$.

Answer:

$15.36$