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Geometry

Law of Cosines Calculator

Find a triangle’s third side from two sides and the included angle.

Use consistent dimensionsArea and volume units explained below

Shape dimensions

Runs on your device

GEOMETRIC RESULT

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter first side, second side, included angle.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Third side = √(a² + b² − 2ab cos C).

A WORKED EXAMPLE

Using first side = 3 m, second side = 4 m, included angle = 90 degrees, the result is 5 m. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.

Common questions

Which inputs does this calculation need?

Find a triangle’s third side from two sides and the included angle. Enter first side in m, second side in m, included angle in degrees. The filled example is editable and is not a saved personal record.

How should I interpret the result?

Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.

Methodology maintained by ClarityKit. How these tools are built and checked.