Which of the following correctly states the Law of Sines for a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$, specifically relating a single pair of side and opposite angle?

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

Answer: (A)

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. For a triangle with sides \(a\), \(b\), and \(c\) opposite angles \(A\), \(B\), and \(C\) respectively, the Law of Sines states that the ratio \(\frac{a}{\sin A}\) is equal to \(\frac{b}{\sin B}\) and also equal to \(\frac{c}{\sin C}\).
3. This means the full Law of Sines can be written as: \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)
4. If the problem asks specifically for the relationship involving a single pair of side and opposite angle, then the correct expression is: \(\frac{a}{\sin A} = \frac{b}{\sin B}\)
5. Note that expressions involving ratios of sides to angles directly (like \(\frac{a}{A}\)) or involving cosine instead of sine do not represent the Law of Sines.