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Law of Cosines Calculator
Solve any triangle using the Law of Cosines: c² = a² + b² − 2ab·cos(C). Handles SAS (find side) and SSS (find angles) configurations.
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The Law of Cosines: c² = a² + b² − 2ab·cos(C). Solves any triangle given SSS or SAS.
Key Features — Law of Cosines Calculator
SAS: find missing side given 2 sides + included angle
SSS: find all angles given 3 sides
Area calculation (SAS and Heron's formula)
Full triangle solution
Triangle inequality validation
Why Use This Tool — Law of Cosines Calculator
Free Online Law of cosines calculatorCosine rule calculator — for EveryoneFast & Easy SAS triangle calculatorSSS triangle solver — 100% FreeFree Online Triangle solver calculator
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Frequently Asked Questions — Law of Cosines Calculator
What is the Law of Cosines?
The Law of Cosines: c² = a² + b² − 2ab·cos(C). It generalizes the Pythagorean theorem to any triangle (when C=90°, cos(90°)=0 and it reduces to c²=a²+b²). Use it when you know two sides and the included angle (SAS) to find the third side, or all three sides (SSS) to find any angle.
How do I find an angle using the Law of Cosines?
Rearranging: cos(C) = (a² + b² − c²) / (2ab). To find angle C, take the inverse cosine: C = arccos((a² + b² − c²) / (2ab)). Similarly for angles A and B. This works for any triangle — you just need all three side lengths.
What is the difference between Law of Sines and Cosines?
Law of Cosines: use for SSS (3 sides) or SAS (2 sides + included angle). It is more robust and avoids the ambiguous case. Law of Sines: use for ASA or AAS (2 angles + a side). Both methods give the same answer when multiple approaches work — choose whichever fits the given information.