Question

value: 2
identify the correct trigonometry formula to use to solve for x.
11
55°
x
a. sin(55°)=\frac{11}{x}
b. sin(55°)=\frac{x}{11}
c. cos(55°)=\frac{11}{x}
d. tan(55°)=\frac{x}{11}

Explanation:

Step1: Recall sine - cosine - tangent definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides relative to the given angle

The angle is $55^{\circ}$, the side opposite to it is not labeled, the side adjacent to it is 11, and the hypotenuse is $x$.

Step3: Select the correct trigonometric ratio

Using the sine formula $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, for $\theta = 55^{\circ}$, $\sin(55^{\circ})=\frac{\text{opposite}}{x}$. Since the opposite side to the $55^{\circ}$ angle is not 11, this is wrong. Using the cosine formula $\cos(55^{\circ})=\frac{11}{x}$ because the adjacent side to the $55^{\circ}$ angle is 11 and the hypotenuse is $x$.

Answer:

C. $\cos(55^{\circ})=\frac{11}{x}$