# Law of cosines Calculator

**Law of cosines** is useful to find the missing information in any triangle

## What is Law of cosines Calculator?

'Cuemath's Law of sines Calculator' is an online tool that helps to calculate the angle of a triangle Cuemath's online Law of sines Calculator is a law applicable to all the triangles and can be used to find unknown angle or length.

NOTE: Please enter the values up to three digits only.

## How to Use Law of cosines Calculator?

Please follow the steps below to find the law of cosines:

**Step 1:**Enter the length of the sides (a,b,c) in the given input box.**Step 2:**Click on the**"Calculate"**button to find the angle subtended by the first side.**Step 3:**Click on the**"Reset"**button to clear the fields and find the angle for different values.

## How to Find Law of cosines Calculator?

A Law of cosines is a law of trigonometry used to calculate angle when three sides are known

**a ^{2}=b^{2}+c^{2}−2bccosA**

**b ^{2}=a^{2}+c^{2}−2accosB**

**c ^{2}=a^{2}+b^{2}−2abcosC**

Where a, b, c are side lengths and A,B,C are angle opposite to them respectively.

**Solved Example:**

Find the length of side for triangle with side length 5, 3, 4 find angle subtended by first side

**Solution:**

Given a = 5, b = 3, b = 4

a^{2}=b^{2}+c^{2}−2bccosA

\(cos A = {{(b^2+c^2-a^2)} \over 2bc}\)

\(cos A = {{(4^2+3^2-5^2)} \over 2.3.4} = 0 \)

A = 90

Similarly, you can try the calculator to find the length of side for the following:

- a = 12, b = 5, c = 13
- a =1 , b = 1, c = 1