# Law of cosines

### From Math Images

(Difference between revisions)

(→Solution) |
|||

Line 42: | Line 42: | ||

===Solution=== | ===Solution=== | ||

- | + | {{hide|1= | |

To find the side length <math>c</math>, | To find the side length <math>c</math>, | ||

Line 103: | Line 103: | ||

[[Image:SAS_solution.jpg]] | [[Image:SAS_solution.jpg]] | ||

+ | }} |

## Revision as of 11:36, 30 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