International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 8, Pages 569-572
doi:10.1155/S016117120000048X

How to generate all integral triangles containing a given angle

Nelson Petulante and Ifeoma Kaja

Department of Mathematics, Bowie State University, Bowie 20715, MD, USA

Received 24 April 1998

Copyright © 2000 Nelson Petulante and Ifeoma Kaja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present an elementary prescription based on the rational secant method for generating all the integral triangles containing a given angle of rational cosine. This is a direct generalization of the ancient problem of finding all the Pythagorean triples. As an example, we discuss a specific equation studied by Diophantus of Alexandria, which turns out to be equivalent to the problem of finding all the integral triangles containing a 60 angle. The material developed here is elementary enough for inclusion in undergraduate courses and advanced high school courses.