# Law of cosines

### From Math Images

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<math>0 = \cos B </math> | <math>0 = \cos B </math> | ||

- | Using [[inverse | + | Using [[Basic Trigonometric Functions#Inverse Trig Functions| inverse trigonometry]], we know that |

<math>B = 90^\circ </math> | <math>B = 90^\circ </math> |

## Revision as of 09:34, 31 May 2011

The law of cosines is a formula that helps in triangulation when two or three side lengths of a triangle are known. The formula relates all three side lengths of a triangle to the cosine of a particular angle.

When to use it: SAS, SSS.

## Contents |

## Proof

Let be oriented so that is at the origin, and is at the point.

### Distance Formula

is the distance from to .

Substituting the appropriate points into the distance formula gives us

Squaring the inner terms, we have

Since ,

Square both sides for

## Example Triangulation

Complete the triangle using the law of cosines.

### Solution