Law of Cosines
Also known as: Cosine Rule
c^2 = a^2 + b^2 - 2ab\cos(C)
c² = a² + b² - 2ab·cos(C)What It Calculates
Generalizes the Pythagorean theorem to any triangle. When C = 90°, cos(C) = 0 and it reduces to a² + b² = c².
variables
| Symbol | Name | Description |
|---|---|---|
| a, b, c | Sides | The three sides of a triangle |
| C | Angle | The angle opposite to side c |
Worked Examples
1
c² = 25 + 49 - 2(5)(7)cos(60°)2
c² = 74 - 70(0.5) = 74 - 35 = 393
c = √39 ≈ 6.24Result: c ≈ 6.24
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Related Formulas
#trigonometry#triangle#advanced