Free Law of Cosines Calculator
Find a side from two sides and the included angle.
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Inputs
Result
Side c
8.1854
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Short answer
Find a side from two sides and the included angle.
What is the Law of Cosines Calculator?
Find a side from two sides and the included angle.
How does the Law of Cosines Calculator work?
Enter the inputs above and read the result.
Formula
Variables
CAngle between sides a and b
Explanation
Generalizes the Pythagorean theorem to any triangle by including the cosine of the included angle.
Examples
Applications
Advantages
Limitations
Common mistakes
Tips
Related concepts
The Law of Cosines Calculator sits inside the Math Calculators hub, in the geometry & shapes cluster. Length, area, volume and angle in two and three dimensions. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Law of Cosines
Find a side from two sides and the included angle. Within math calculators, law of cosines belongs to the geometry & shapes cluster, where it shares terminology and assumptions with closely related tools.
Learning how law of cosines is calculated
Generalizes the Pythagorean theorem to any triangle by including the cosine of the included angle. Working through the variables one at a time — C — makes the result reproducible by hand and easier to sanity-check.
Using law of cosines to make a decision
Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How law of cosines compares with related measures
area, perimeter, volume, surface area all describe adjacent aspects of geometry & shapes. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
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