1. Objectives:
1. Use the law of cosines to find unknown
parts of a triangle.

2. When to use Law of Cosines
We know both SAS and SSS
determine unique triangles.
Law of Cosines can be used to solve
a triangle for either case.

3. Deriving Law of Cosines
By the distance formula:

4. Example 1:
Two sides of a triangle have lengths 3
cm and 7 cm and the angle between
them is 130°. Find the length of the
third side.

5. Alternate Form
Solving the law of cosines for cos C
gives:
which is used to find angles when all 3
side lengths are given.

6. Example 2:
The lengths of the sides of a triangle
are 5, 10, and 12. Solve the triangle.

7. Example 3:
Find AD.

8. You Try!
A triangle has side lengths 6, 12 and
15. Find the length of the median to
the longest side.

9. What to Use: