Law of Cosines Calculator

This calculator applies the law of cosines and writes the substitution out one line at a time. Enter two sides and the angle between them to get the third side, or enter all three sides and pick the angle you want back. Each result carries the rule, the numbers put into it, the squares, the product, and the closing square root or inverse cosine. It stops there on purpose: it never uses the sine rule and does not finish the remaining angles, so reach for the trigonometry calculator when you want the whole triangle solved.

Calculator Type

Give the two sides that meet at the known angle. Every line of the substitution is shown.

The angle where sides b and c meet. Side a is the one facing it.
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Give all three sides and pick the angle you want. The rearranged rule is shown step by step.

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