1. 13.5 Law of Cosines Objectives: 1.Solve problems by using the Law of Cosines 2.Determine whether a triangle can be solved by first using the Law of Sines or the Law of Cosines

2. Law of Cosines The Law of Cosines is used to solve a triangle when you are given two sides and the included angle or when you know all 3 sides. Let ΔABC be any triangle with a, b, and c representing the measures of sides and opposite angles with measures A, B, and C, respectively. Then the following equations are true:

3. Recall the Law of Sines The Law of sines is used when you have an angle and its opposite side and another side or angle. Once you use the law of cosines, you may be able to use the law of sines to finish the problem if you have the appropriate information.

4. Example Solve ΔABC C=73°, b=10, a=7 c²=a²+b²-2ab cos C c²=7²+10²-2(7)(10) cos 73 c²=149-140 cos 73 c²=108 c=10.4 Now use L of S

5. Example Solve ΔABC. a=9, b=7, c=12

6. Homework p 736 10-26 even