If two triangles are similar, which of the following statements about the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ is always true for both triangles?

• A. The angles of both triangles are different.
• B. The ratios $\frac{a}{sin\left(A\right)}$, $\frac{b}{sin\left(B\right)}$, and $\frac{c}{sin\left(C\right)}$ are equal in both triangles.
• C. The $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ does not apply to similar triangles.
• D. The side lengths of both triangles are equal.

Answer: (B)

Verified step by step guidance

1. Recall that similar triangles have the same angles but their corresponding sides are proportional, not necessarily equal.
2. The Law of Sines states that for any triangle with sides \(a\), \(b\), and \(c\) opposite angles \(A\), \(B\), and \(C\) respectively, the following ratio holds: \(\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}\).
3. Since the triangles are similar, their corresponding angles \(A\), \(B\), and \(C\) are equal, so the sine values \(\sin(A)\), \(\sin(B)\), and \(\sin(C)\) are the same for both triangles.
4. Because the sides are proportional, the ratios \(\frac{a}{\sin(A)}\), \(\frac{b}{\sin(B)}\), and \(\frac{c}{\sin(C)}\) will be equal within each triangle but scaled by the similarity ratio between the two triangles.
5. Therefore, the ratios \(\frac{a}{\sin(A)}\), \(\frac{b}{\sin(B)}\), and \(\frac{c}{\sin(C)}\) are equal for each triangle individually, but when comparing the two similar triangles, these ratios are proportional by the scale factor of similarity.