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, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. The angle $\theta = 55^{\circ}$, the side adjacent to the $55^{\circ}$ angle is 11 and the hypotenuse is $x$.

Step2: Select the correct trigonometric ratio

Since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, for $\theta = 55^{\circ}$, adjacent side = 11 and hypotenuse = $x$, we have $\cos(55^{\circ})=\frac{11}{x}$.

Answer:

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