Law of cosines
Generalises the Pythagorean theorem to any triangle. History: Euclid's Elements, c. 300 BC.
How to work it out
- 1
The statement:
- 2
Generalises the Pythagorean theorem to any triangle.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ c^2 = a^2 + b^2 - 2ab\cos C \]
Third side when a = 5 and b = 7 (computed)
| Angle C | c |
|---|---|
| 30° | 3.6576 |
| 60° | 6.2450 |
| 90° | 8.6023 |
| 120° | 10.4403 |
| 150° | 11.6027 |
Questions
What is the law of cosines?
Generalises the Pythagorean theorem to any triangle.
Who is the Law of cosines associated with?
Euclid.