How is the sine rule expressed for finding unknown angles?

The sine rule, also known as the law of sines, expresses a relationship between the lengths of the sides of a triangle and the sines of its angles. It is particularly useful in solving problems related to non-right triangles, allowing us to find unknown angles or sides when we have enough information.

The correct expression given reflects the relationship where the ratio of the sine of each angle to the length of the opposite side is constant across all three angles and sides of the triangle. In mathematical terms, this is represented as:

[

\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

]

Here, A, B, and C are the angles of the triangle, while a, b, and c are the lengths of the sides opposite these angles respectively. This equality can be utilized to find unknown angles if the lengths of the sides are known, or to find missing side lengths if the angles are known.

The other choices presented do not accurately represent the sine rule as it pertains to finding unknown angles or sides. For instance, one option suggests a formula that implies a relationship not consistent with the law of sines. Thus, the complete and accurate format of the sine rule