Given triangle $GFE$, which equation can be used to find the measure of angle $GFE$ using the Law of Sines?

• A. $\frac{\sin \left(GFE\right)}{fg}=\frac{\sin \left(FEG\right)}{ge}$
• B. $\frac{ge}{\sin \left(GFE\right)}=\frac{fg}{\sin \left(FEG\right)}$
• C. $\frac{\sin \left(GFE\right)}{ge}=\frac{\sin \left(FEG\right)}{fg}$
• D. $\frac{\sin \left(GFE\right)}{fe}=\frac{\sin \left(FGE\right)}{ge}$

Answer: (C)

Verified step by step guidance

1. Recall the Law of Sines, which states that in any triangle, the ratio of the sine of an angle to the length of the side opposite that angle is constant. Mathematically, this is expressed as \(\frac{\sin(\text{angle})}{\text{opposite side}} = \frac{\sin(\text{another angle})}{\text{its opposite side}}\).
2. Identify the angle you want to find, which is angle \(GFE\), and the side opposite to it. In triangle \(GFE\), the side opposite angle \(GFE\) is \(ge\).
3. Choose another angle and its opposite side to set up the Law of Sines ratio. For example, angle \(FEG\) and its opposite side \(fg\).
4. Write the Law of Sines equation using these identified angles and sides: \(\frac{\sin(GFE)}{ge} = \frac{\sin(FEG)}{fg}\).
5. Use this equation to solve for \(\sin(GFE)\) or directly for angle \(GFE\) by applying the inverse sine function after substituting known side lengths and angle measures.