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.



Examples







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.



Examples










Area Formulas

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

Area .



Examples