In the Law of Sines for a triangle, which statement is true?

• A. (AB) / Sin(C) = (BC) / Sin(A)
• B. (BC) / Sin(B) = (AC) / Sin(C)
• C. (AC) / Sin(A) = (AB) / Sin(C)
• D. All of the above are true

Answer: (D)

The Law of Sines states that the ratios of the lengths of the sides of a triangle to the sines of their opposite angles are equal. Specifically, for any triangle with sides opposite to angles A, B, and C, the relationship can be expressed as:

[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} ]

Where ( a ), ( b ), and ( c ) are the lengths of the sides opposite to angles A, B, and C, respectively.

In the context of this question, the provided statements effectively embody several formulations of the Law of Sines. Each equation presented is a valid representation of the relationship defined by the Law of Sines.

The first statement describes the ratio of side AB to the sine of angle C being equal to the ratio of side BC to the sine of angle A. This matches the structure of the Law of Sines and illustrates how the sides and angles relate to one another.

The second statement similarly expresses that the ratio of side BC to the sine of angle B is equal to the ratio of side AC to the sine of angle C, further exemplifying the application of the law for