Question

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

Explanation:

Step1: Use the tangent function

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

Step2: Solve for $x$

Rearrange the equation: $x=\frac{4}{\tan(12^{\circ})}$.
We know that $\tan(12^{\circ})\approx0.2126$. Then $x=\frac{4}{0.2126}$.

Step3: Calculate the value of $x$

$x=\frac{4}{0.2126}\approx18.82$.

Answer:

$18.82$