Grade 11 · Mathematics
Cosine law
Why it matters
Solving oblique triangles.
Core20m readingPrerequisite: Sine law
What is the cosine law?
Short answer
The cosine law (law of cosines) relates the three sides of any triangle to one of its angles: c² = a² + b² − 2ab·cos C. It generalizes the Pythagorean theorem to non-right triangles and is used to find a third side from two sides and the included angle, or to find an angle when all three sides are known.
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Frequently asked questions
- When do you use the cosine law instead of the sine law?
- Use the cosine law when you know two sides and the included angle, or all three sides; the sine law needs an angle–opposite-side pair.
- How does the cosine law relate to the Pythagorean theorem?
- When the angle is 90°, cos C = 0, so it reduces to c² = a² + b².