Given triangle $FGE$ with sides $f$, $g$, and $e$ opposite angles $F$, $G$, and $E$ respectively, which equation can be used to find the measure of angle $FGE$ using the Law of Sines?

• A. $\frac{f}{sinG}=\frac{g}{sinF}$
• B. $\frac{g}{sinG}=\frac{e}{sinE}$
• C. $\frac{e}{sinE}=\frac{f}{sinF}$
• D.

Answer: (B)

Verified step by step guidance

1. Recall the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Mathematically, this is expressed as: \(\frac{f}{\sin\ F} = \frac{g}{\sin\ G} = \frac{e}{\sin\ E}\).
2. Identify the sides and angles given: side \(f\) is opposite angle \(F\), side \(g\) is opposite angle \(G\), and side \(e\) is opposite angle \(E\).
3. To find the measure of angle \(FGE\), which corresponds to angle \(G\) in triangle \(FGE\), set up the Law of Sines ratio involving side \(g\) and angle \(G\).
4. Use the equality of ratios from the Law of Sines to relate side \(g\) and angle \(G\) to another known side and its opposite angle, for example side \(e\) and angle \(E\): \(\frac{g}{\sin\ G} = \frac{e}{\sin\ E}\).
5. From this equation, you can solve for \(\sin\ G\) or directly find angle \(G\) by taking the inverse sine once the values of sides \(g\) and \(e\) and angle \(E\) are known.