Implementing the Law of Sines to solve SAS triangles

TL;DR

This paper presents an alternative method for solving SAS triangles using the Law of Sines instead of the traditional Law of Cosines, supported by proofs and detailed examples.

Contribution

It introduces a novel approach to solving SAS triangles by applying the Law of Sines, providing proofs and practical examples as an alternative to the standard Law of Cosines method.

Findings

The Law of Sines can be effectively used to solve SAS triangles.

The approach is supported by mathematical proofs and detailed examples.

This method offers an alternative perspective in trigonometry problem-solving.

Abstract

By "solving a triangle", one refers to determining the three sidelengths and the three angles, based on given information.Depending on the specific information, one or more triangles may satisfy the requirements of the given information.In the SAS case, two of sidelengths are given, as well as the angle contained by the two sides.According to Euclidean Geometry, such a triangle must be unique. In reference [1], and pretty much in standard trigonometry and precalculus texts,the Law of Cosines is employed in solving a SAS triangle. In this work we use an alternative approach by using the Law of Cosines.In Section 2, we list some basic trigonometric identities and in Section 3 we prove a lemma which is used in Section4. In Section4, we demonstrate the use of the Law of Sines in solving an SAS triangle. In Section 5 we offer three examples in detail; the last one being more general in nature.