1. Copyright © 2011 Pearson, Inc. 5.6 Law of Cosines Goal: Apply the Law of Cosines.

2. Copyright © 2011 Pearson, Inc. Slide 5.6 - 2 What you’ll learn about Solving Triangles (SAS, SSS) Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.

3. Copyright © 2011 Pearson, Inc. Slide 5.6 - 3 Law of Cosines

4. Copyright © 2011 Pearson, Inc. Example: Solving a Triangle Solve the triangle. Slide 5.6 - 4

5. Copyright © 2011 Pearson, Inc. Example: Solving a Triangle Solve the triangle. Slide 5.6 - 5

6. Copyright © 2011 Pearson, Inc. A New Area Formula!

7. Copyright © 2011 Pearson, Inc. Slide 5.6 - 7 Area of a Triangle

8. Copyright © 2011 Pearson, Inc. SAS Area Example #1 The diagram at the right shows a triangular playground that is bounded by Main Street, High Street, and Central Street. The Park District has hired a contractor to pave the surface of the playground with asphalt. What is the area of the playground to the nearest foot?

9. Copyright © 2011 Pearson, Inc. SAS Area Example #2 Two adjacent sides of a triangle are 4cm and 6cm in length, the angle between them is 76°. Find the area of the triangle to the nearest thousandth.