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
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 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