The Law of Sines and Cosines

Law of Sines

For any Triangle with sides a, b, c opposite angles A, B, C:

a/sin A = b/sin B = c/sin C

Use when you know: AAS, ASA, or SSA (two angles and a side, or two sides and an Angle opposite one of them).

Law of Cosines

For any Triangle:

c² = a² + b² − 2ab cos C

Use when you know: SAS or SSS (two sides and included Angle, or all three sides).

When to Use Which

• Law of Sines: When you have Angle-side pairs (AAS, ASA, SSA).
• Law of Cosines: When you have SAS or SSS.
• Note: The Pythagorean Theorem is a special case of the Law of Cosines when C = 90°.