USING LAW OF COSINES WITH A SIDE-SIDE-ANGLE TRIANGLE

Abstract

The purpose of this paper is to demonstrate that Law of Cosines may be used when working with a Side-Side-Angle (SSA) triangle. These types of triangles usually use the Law of Sines to solve due to the easier arithmetic route but add in conditions to test to determine the number of triangles formed from the measurements. This can be met with resistance from some students who prefer formulas over additional conditions. Students have asked if there was an “all-encompassing” formula to apply when solving triangles. These students preferred formulas to memorize over lists of conditions to apply. It was answering this question that sparked the motivation for this paper.

While this paper does not answer the question of an “all-encompassing” formula, I was aware that Law of Cosines may be used when confronted with an SSA situation. The question I answer here is, “How can it be used?” Another question is, “Does it make it easier to solve SSA triangles?” The answer is ambiguous unfortunately. It can be used. If you are interested in another formula to determining the missing side of an SSA triangle, then this paper presents a formula. This formula combines the conditions for how many triangles you have, but we sacrifice simplicity arithmetically.

Received: March 1, 2025
Accepted: March 27, 2025