Question

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

Explanation:

Step1: Recall sine - cosine definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $FGE = x$, 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 have $\sin(x)=\frac{9}{15.2}$.

Answer:

$\sin(x)=\frac{9}{15.2}$ (corresponding to the second option in the multiple - choice list)