The Sine and Cosine Rules

The Sine Rule

The sine rule is useful for solving triangles when:
- We know two angles and one side (AAS or ASA)
- We know two sides and one non-included angle (SSA), but beware of the ambiguous case
An understanding of the ambiguous case of the sine rule is important:
- The ambiguous case happens when, given two sides (a, b) and an angle (A) opposing one of them, there are two possibilities for the triangle.
- This is because the sin function has two solutions (one in the first quadrant and one in the second quadrant) between 0 and 180 degrees
Remember, the formula of the sine rule is as follows:
- (a / sin A) = (b / sin B) = (c / sin C)

The cosine rule is useful for solving triangles when:
- We know three sides (SSS) or
- Two sides and the included angle (SAS)
Familiarise with the formula of the cosine rule, which is as follows:
- c² = a² + b² - 2ab cosC
Practise manipulation of the cosine rule
- One modified form of the rule allows you to find an angle when you know all three sides: cos C = (a² + b² - c²) / 2ab.

Use these rules in diversified problems and consolidate these skills with problem solving.