Question

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

Explanation:

Step1: Identify sides relative to $x$

In right $\triangle FEG$, $\angle G = x$.

• Hypotenuse: $FG = 15.2$ m
• Opposite side to $x$: $FE = 9$ m

Step2: Apply sine definition

Sine of an angle in a right triangle is $\frac{\text{Opposite}}{\text{Hypotenuse}}$.
$\sin(x) = \frac{9}{15.2}$

Answer:

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