Two laws that solve any triangle — not just right ones.
Walk through
Step 1 of 5
The problem
A triangle has sides a = 7 and b = 9 with the angle C = 50° between them. Find side c.
Which law, when?
- Law of Sines — when you know an angle and its opposite side, plus one more angle or side (AAS, ASA, or the tricky SSA case).
- Law of Cosines — when you know two sides and the included angle (SAS), or all three sides (SSS).
- Cosine law with C = 90° collapses to Pythagoras, since cos 90° = 0.
Your turn
In a triangle, a = 8, A = 30°, B = 45°. Find side b.
Watch out
The SSA ('ambiguous') case: when you're given two sides and a non-included angle, there can be two valid triangles. Always check whether 180° − your angle also works.
Law of sines
Law of cosines
Cosine law generalises Pythagoras — when C = 90°, cosC = 0 and you're back to a² + b² = c².