Question

What are the two cases in which the Laws of Sines can be applied to solve a non-right triangle?

Case I. You know the measures of two angles and any side of the triangle.
Case II. You know the measures of two sides and an angle opposite one of the two known sides.
Case III. You know the measures of two sides and the included angle.
Case IV. You know the measures of all three sides.

Answer 1

Case I, Case II

Explanation:

For cases III and IV, you need the Law of Cosines.

The Law of Sines can be used when you have at least one side and the angle opposite. If you know two angles of a triangle, you know all three, so the given angles don't necessarily have to be opposite the given side if two angles are known.

The Laws of Sines can be applied to solve Case I and Case II.