Question

find the measure of x.
18
65°
x
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, $\theta = 65^{\circ}$, the hypotenuse is $18$, and the adjacent side to the $65^{\circ}$ angle is $x$. So, $\cos(65^{\circ})=\frac{x}{18}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(65^{\circ})=\frac{x}{18}$ by $18$. We get $x = 18\times\cos(65^{\circ})$.
Using a calculator, $\cos(65^{\circ})\approx0.4226$. Then $x=18\times0.4226 = 7.6068$.

Answer:

$7.61$