Which equation correctly expresses the Law of Sines for a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, and $C$?

• A. $\frac{a}{b}=\frac{c}{A}$
• B. $\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$
• C. $\frac{a}{A}=\frac{b}{B}=\frac{c}{C}$
• D. $\frac{a}{cosA}=\frac{b}{cosB}=\frac{c}{cosC}$

Answer: (B)

Verified step by step guidance

1. Recall that the Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles.
2. Identify the sides and their opposite angles: side \(a\) is opposite angle \(A\), side \(b\) is opposite angle \(B\), and side \(c\) is opposite angle \(C\).
3. Write the Law of Sines formula, which states that the ratio of a side length to the sine of its opposite angle is the same for all three sides:
4. \[\frac{a}{\sin\left(A\right)} = \frac{b}{\sin\left(B\right)} = \frac{c}{\sin\left(C\right)}\]
5. This equation correctly expresses the Law of Sines and can be used to solve for unknown sides or angles in a triangle.