Law of Cosines Calculator
Solve a triangle side using the law of cosines.
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Introduction
Law of Cosines Calculator — Solve a triangle side using the law of cosines. Enter Side a, Side b, Included angle C (degrees) to get an instant, accurate result.
Formula
Law of cosines: c² = a² + b² − 2ab×cos(C), solved for side c given two sides a, b and their included angle C (in degrees).
Step-by-step
- Enter the Side a.
- Enter the Side b.
- Enter the Included angle C (degrees).
- Click Calculate to see your result instantly.
Real-world example
Example: With Side a = 3, Side b = 4, Included angle C (degrees) = 90, the Law of Cosines Calculator gives Side C: 5.
Frequently Asked Questions
When should I use law of cosines instead of law of sines?
Law of cosines is ideal when you know two sides and the angle between them (SAS), which law of sines can't directly solve.
Does this reduce to the Pythagorean theorem?
Yes — when C = 90°, cos(C) = 0 and the formula becomes c² = a² + b².
What inputs does the Law of Cosines Calculator need?
You'll need to provide: Side a, Side b, Included angle C (degrees). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Law of Cosines Calculator?
The Law of Cosines Calculator applies the formula exactly as calculated — Law of cosines: c² = a² + b² − 2ab×cos(C), solved for side c given two sides a, b and their included angle C (in degrees). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Law of Cosines Calculator free to use?
Yes, the Law of Cosines Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Law of Cosines Calculator
The Law of Cosines Calculator uses a real, verifiable formula — Law of cosines: c² = a² + b² − 2ab×cos(C), solved for side c given two sides a, b and their included angle C (in degrees). — so results are accurate every time, not an approximation.