Section 3.2 Law of Cosines

Section Objectives

  1. Use the Law of Cosines to solve triangles.
  2. Use the Law of Cosines in applications.
  3. Use Heron's formula to find the area of a triangle.



Law of Cosines

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 Cosines says that

.



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



Examples










Heron's Area Formula

Heron's formula for the area of can be derived from the Law of Cosines:

Area , where is the semi-perimeter of the triangle with sides of lengths , , and .



Examples