Trigonometry

Law of Cosines - Trigonometry

Learn the law of cosines with examples, step-by-step guide, and calculator tools. Relate all three sides and one angle in a triangle

The law of cosines is a fundamental concept in trigonometry. Relate all three sides and one angle in a triangle. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[c^2 = a^2 + b^2 - 2ab\cos C\]

Variables

a, b, c
Side lengths
C
Angle between sides a and b

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [] → If a=5, b=7, C=60°, then c = √(25 + 49 - 2×5×7×0.5) = √39 ≈ 6.24

Example 2

Example 2: 6.24

Frequently Asked Questions

What is the law of cosines?

Relate all three sides and one angle in a triangle

How do I calculate law of cosines?

Use the formula: c^2 = a^2 + b^2 - 2ab\cos C. Follow the steps provided above.

What tools can help with law of cosines?

We provide online calculators: calculator

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