Question

value: 2
identify the correct trigonometry formula to use to solve for x.
62° x
18
a. sin(62°) = \frac{18}{x}
b. sin(62°) = \frac{x}{18}
c. cos(62°) = \frac{18}{x}
d. tan(62°) = \frac{x}{18}

Explanation:

Step1: Recall trigonometric ratios

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 side opposite the $62^{\circ}$ angle is not given, the side adjacent to the $62^{\circ}$ angle is 18, and the hypotenuse is $x$.

Step2: Select the correct ratio

Since we know the adjacent side and the hypotenuse with respect to the $62^{\circ}$ angle, we use the cosine ratio $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(62^{\circ})=\frac{18}{x}$.

Answer:

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