Question

which equation can be used to find the measure of angle fge? options: \\(\sin(x) = \frac{15.2}{9}\\), \\(\sin(x) = \frac{9}{15.2}\\), \\(\cos(x) = \frac{15.2}{9}\\), \\(\cos(x) = \frac{9}{15.2}\\). diagram: right triangle feg with right angle at e, fe = 9m, fg = 15.2m, angle at g is x.

Explanation:

Step1: Identify triangle parts

In right triangle \( \triangle FEG \), \( \angle E = 90^\circ \), opposite to \( \angle x \) (angle \( FGE \)) is \( FE = 9 \, \text{m} \), hypotenuse \( FG = 15.2 \, \text{m} \).

Step2: Recall sine definition

Sine of an angle in a right triangle is \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \). For \( \angle x \), opposite side is \( 9 \), hypotenuse is \( 15.2 \), so \( \sin(x) = \frac{9}{15.2} \).

Answer:

\(\sin(x) = \frac{9}{15.2}\) (corresponding option: the one with \(\sin(x) = \frac{9}{15.2}\))