Analysis of proof |

Now we can write the law of cosines for the perimeter of the triangle.

Law of cosines for perimeter |

The result is a very simple and beautiful formula that describes the entire triangle.

**The law of cosines shows a relationship between the angles and the lengths of the sides of a triangle.**

The geometry of the law of cosines |

Law of cosines for perimeter describes the perimeter of the triangle made up of one-dimensional Euclidean spaces. For multidimensional spaces cosine law has a different view.

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