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 given angle is $62^{\circ}$, the side opposite to it has length 18 and the hypotenuse has length $x$.

Step2: Select the correct ratio

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

Answer:

A. $\sin(62^{\circ})=\frac{18}{x}$