Question

identify the correct trigonometry formula to use to solve for x.
18
a. sin(62°) = 18/x
b. sin(62°) = x/18
c. cos(62°) = 18/x
d. tan(62°) = x/18

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. The angle $\theta = 62^{\circ}$, the side adjacent to the $62^{\circ}$ angle is 18, and the hypotenuse is $x$.

Step2: Select the correct formula

Since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, for $\theta = 62^{\circ}$, adjacent = 18 and hypotenuse = $x$, we have $\cos(62^{\circ})=\frac{18}{x}$.

Answer:

C. $\cos(62^{\circ})=\frac{18}{x}$