Question

which equation could be used to find the value of x?
cos 49° = \frac{x}{55}
cos 49° = \frac{55}{x}
sin 49° = \frac{x}{55}
sin 49° = \frac{55}{x}

Explanation:

Step1: Recall trigonometric - ratio definitions

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

Step2: Identify sides relative to the given angle

For the right - triangle with angle $49^{\circ}$, the side opposite to the $49^{\circ}$ angle is the side with length $x$, and the hypotenuse has length $55$.

Step3: Select the correct trigonometric equation

Using the sine ratio $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, when $\theta = 49^{\circ}$, we have $\sin49^{\circ}=\frac{x}{55}$.

Answer:

$\sin49^{\circ}=\frac{x}{55}$ (the option that reads $\sin49^{\circ}=\frac{x}{55}$)