How to use the law of cosines calculator
Find the third side from two sides and the included angle. Enter side a, side b, included angle c in the fields above; the side c, area are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “cosine rule”, “sas triangle”, “third side”, “calculate law of cosines”, “find side c”.
Formula
Variables
- a — Side a
- b — Side b
- C — Included angle C (°)
Worked example
With side a = 8, side b = 11, included angle c = 50 °, the calculator gives side c ≈ 8.477581; area ≈ 33.70596.
Frequently asked questions
What is the law of cosines calculator used for?
Find the third side from two sides and the included angle. It helps with questions such as “cosine rule”, “sas triangle”, “third side”.
What is the formula for the law of cosines calculation?
Side c = √(a × a+b × b-2 × a × b × cos(C)). Area = 0.5 × a × b × sin(C). Here a is side a, b is side b, C is included angle c (°).
What inputs do I need for the law of cosines calculator?
You need side a, side b, included angle c in °. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the law of cosines calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the law of cosines result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.