Question

which equation can be used to find the measure of angle fge? sin(x) = 15.2/9, sin(x) = 9/15.2, cos(x) = 15.2/9, cos(x) = 9/15.2

Explanation:

Step1: Recall sine - cosine definitions in right - triangle

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In right - triangle $FEG$ with right - angle at $E$, for angle $x$ (angle $G$), the side opposite to angle $x$ is $FE = 9$ m and the hypotenuse is $FG=15.2$ m.

Step2: Determine the correct trigonometric ratio

Using the sine definition $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$, we substitute the values of the opposite side and the hypotenuse. So, $\sin(x)=\frac{9}{15.2}$.

Answer:

$\sin(x)=\frac{9}{15.2}$