When using the Law of Sines to solve a triangle, which of the following equations is correct?

• A. $\frac{\sin A}{b}=\frac{\sin B}{c}=\frac{\sin C}{a}$
• B. $\frac{a}{b}=\frac{c}{\sin A}$
• C. $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$
• D. $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Answer: (C)

Verified step by step guidance

1. Recall the Law of Sines, which relates the sides and angles of a triangle. It states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles in the triangle.
2. Write the Law of Sines formula as: \(\frac{a}{\sin\ A} = \frac{b}{\sin\ B} = \frac{c}{\sin\ C}\), where \(a\), \(b\), and \(c\) are the sides opposite angles \(A\), \(B\), and \(C\) respectively.
3. Notice that the ratio can be written with sine in the numerator or denominator, but the correct and standard form places the side length in the numerator and the sine of the opposite angle in the denominator, or equivalently, the sine of the angle in the numerator and the side length in the denominator.
4. Compare the given options carefully: the correct equation must maintain the correspondence between each side and its opposite angle, ensuring the ratios are equal.
5. Conclude that the correct form is \(\frac{\sin\ A}{a} = \frac{\sin\ B}{b} = \frac{\sin\ C}{c}\), which matches the standard Law of Sines expression.