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

feet, feet, feet. Solve the triangle. (This is an SSS case.)

meters, meters, . Solve the triangle. (This is an SAS case.)

#49, page 276.

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

Find the area of a triangular in the first example above.