Section 3.1 Law of Sines

Section Objectives

  1. Use the Law of Sines to solve triangles.
  2. Find the area of a triangle.
  3. Use the Law of Sines in applications.

Law of Sines

Suppose is a triangle with sides of lengths , , and that are opposite their respective vertices , , and . Let , , and be the angles at , , and . The Law of Sines says that


When the appropriate information is known, the Law of Sines can be used to solve triangles.


The Ambiguous Case (SSA or ASS)

A triangle is not necessarily uniquely determined in the SSA (ASS) case. There are three possibilities:

When solving triangles, always keep in mind that the longer sides lie opposite the larger angles.


Area Formulas

It is pretty easy to derive these formulas for the area of :

Area .