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Law of Cosines Calculator

Math

Find the third side of a triangle given two sides and the included angle, using the law of cosines.

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01,000,000
01,000,000
0.01179.98

Side c

4.0000

The length of the third side, opposite the included angle, c^2 = a^2 + b^2 - 2ab*cos(gamma).

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Odeh Ahwal

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Odeh Ahwal
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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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