Which of the following correctly states the Law of Sines for triangle $ABC$ with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$?

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

Answer: (A)

Verified step by step guidance

1. Recall that the Law of Sines relates 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: \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\).
4. Compare this formula to the given options to determine which one correctly expresses the Law of Sines.
5. Note that the correct expression must have sides in the numerator and the sine of the opposite angles in the denominator, all equal to each other.