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.

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.