Equations · equation
Law of Cosines
Vectors & Geometry · c. 300 BCE
- Equation
- c² = a² + b² − 2ab cos C
- Field
- Vectors & Geometry
- Symbols
- a, b, c the three sides of any triangle · C the angle opposite side c
- Year
- -300
Significance
Pythagoras for triangles that are not right-angled: the correction term vanishes when C = 90°. It is what a surveyor uses to close a triangle from two sides and the included angle, what a navigator uses for a course change, and what the dot product's cosine form is a restatement of. Euclid proved it geometrically in the Elements; al-Kashi wrote it with a cosine in 1427.
Referenced by
equation
skill
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.