Question

which equation can be used to find the measure of angle fge?

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

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

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

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

Explanation:

Step1: Recall the definition of sine function

In a right - triangle, \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\).
For angle \(x\) (angle \(FGE\)), the side opposite to angle \(x\) is \(FE = 9\) m and the hypotenuse is \(FG=15.2\) m.

Step2: Apply the sine formula

Substitute the values into the sine formula: \(\sin(x)=\frac{FE}{FG}\).

Answer:

\(\sin(x)=\frac{9}{15.2}\) (the second option)