Question

find the measure of x. 62° 8 x = ? round to the nearest hundredth

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 62^{\circ}$, the adjacent side to the $62^{\circ}$ angle is $8$, and the hypotenuse is $x$. So, $\cos(62^{\circ})=\frac{8}{x}$.

Step2: Solve for \(x\)

Rearrange the equation $\cos(62^{\circ})=\frac{8}{x}$ to get $x=\frac{8}{\cos(62^{\circ})}$.
We know that $\cos(62^{\circ})\approx0.469569$.
Then $x=\frac{8}{0.469569}\approx17.04$.

Answer:

$17.04$