Question

find the measure of x. round to the nearest hundredth

Explanation:

Step1: Use tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 42^{\circ}$, the opposite side to the $42^{\circ}$ angle is $17$ and the adjacent side is $x$. So, $\tan(42^{\circ})=\frac{17}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{17}{\tan(42^{\circ})}$. Since $\tan(42^{\circ})\approx0.9004$, then $x=\frac{17}{0.9004}\approx18.88$.

Answer:

$18.88$