Question

identify the correct trigonometry formula to use to solve for x.

a. $sin(55^{circ})=\frac{11}{x}$
b. $sin(55^{circ})=\frac{x}{11}$
c. $cos(55^{circ})=\frac{11}{x}$
d. $\tan(55^{circ})=\frac{x}{11}$

Explanation:

Step1: Recall sine - cosine - tangent 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 $\theta = 55^{\circ}$, the side opposite to the $55^{\circ}$ angle is the vertical side of length 11, and the hypotenuse is of length $x$.

Step2: Apply the sine formula

Since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, substituting $\theta = 55^{\circ}$, opposite = 11 and hypotenuse = $x$, we get $\sin(55^{\circ})=\frac{11}{x}$.

Answer:

A. $\sin(55^{\circ})=\frac{11}{x}$