The Cosine Law by Similarity

The Law of Cosines establishes a relationship between the angles and the side lengths of \(\Delta ABC\):

\(c^{2} = a^{2} + b^{2} - 2ab\cdot \mbox{cos}\gamma,\)

where \(\gamma\) is the angle in \(\Delta ABC\) opposite side \(c\).

Cosine Law by Similarity - proof without words

This proof without words submitted by Anders Kaseorg combines together \(3\) similar triangles; but where is the third? The proof was actually published at the American Mathematical Monthly, 121, February 2014, p 149, by Miles Dillon Edwards.

(There are several theorems that are proved by similar technique.)

|Contact| |Front page| |Contents| |Geometry| |Up| |Store|

Copyright © 1996-2017 Alexander Bogomolny

 62038554

Search by google: