1. The Law of Cosines

2. When To Use The Law of Cosines
The Law of Cosines can be used to find
an angle if the three sides of a triangle are known
the side of a triangle if two sides and the included angle are known

3. Three Sides Known We know the lengths of the sides of a triangle:
(If you’re a real slick math student, you already recognize that this is a 30 – 60 – 90 triangle, but let’s use the Law of Cosines to prove it!)

5. Finding the Other Angles
To find angle B, use the alternate form of the Law of Cosines:
To find angle C, use the fact that the sum of the angles of a triangle is 180.

6. Two Sides and an Included Angle Known
We know the following information about a triangle:
(If you’re a real slick math student, you already recognize that this is a 45 – 45 – 90 triangle, but let’s use the Law of Cosines to prove it!)

7. Let’s find side c first:

8. Finding the Other Angles
To find angle B, use the alternate form of the Law of Cosines:
To find angle C, use the fact that the sum of the angles of a triangle is 180.