Law of Cosines

Pythagoras for every triangle

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Law of cosines: $c^2 = a^2 + b^2 - 2ab\cos C$.
• At C = 90° it becomes Pythagoras. Smaller angles give shorter sides, larger angles longer ones.
• Rearranged, it finds any angle from three sides: $\cos C = \frac{a^2 + b^2 - c^2}{2ab}$.

Steps

1. Close the hinge
2. Watch the third side
3. The law of cosines
4. At 60°
5. At 120°
6. Flat out
7. Find an angle