# 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

• 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.