Law of Cosines Calculator
MathFind the third side of a triangle given two sides and the included angle, using the law of cosines.
Side c
The length of the third side, opposite the included angle, c^2 = a^2 + b^2 - 2ab*cos(gamma).
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
What is the law of cosines?
It generalizes the Pythagorean theorem to any triangle, not just right triangles: c^2 = a^2 + b^2 - 2ab*cos(gamma), where gamma is the angle between sides a and b.
How does this relate to the Pythagorean theorem?
When gamma is 90 degrees, cos(gamma) = 0, and the formula reduces exactly to the Pythagorean theorem, c^2 = a^2 + b^2.
Can this calculator go the other direction, finding an angle from three known sides?
Not this version, it is scoped to the two-sides-plus-included-angle case (SAS). Solving all three angles from three known sides (SSS) uses the same formula rearranged to solve for the angle instead, but needs a different fixed set of inputs.
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