Question

find the measure of x. round to the nearest hundredth

Explanation:

Step1: Identify trigonometric relation

We use cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 62^{\circ}$, adjacent side to $62^{\circ}$ is 8 and hypotenuse is $x$. So $\cos62^{\circ}=\frac{8}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{8}{\cos62^{\circ}}$. Since $\cos62^{\circ}\approx0.4695$, then $x = \frac{8}{0.4695}\approx17.04$.

Answer:

$17.04$