# High School Math : Applying the Law of Cosines

## Example Questions

### Example Question #1 : Applying The Law Of Cosines

In  , , and . To the nearest tenth, what is ?   A triangle with these sidelengths cannot exist.  Explanation:

By the Triangle Inequality, this triangle can exist, since .

By the Law of Cosines: Substitute the sidelengths and solve for :      ### Example Question #11 : Graphing The Sine And Cosine Functions

A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?      Explanation:

We can apply the Law of Cosines to find the measure of this angle, which we will call : The widest angle will be opposite the side of length 22, so we will set:        ### Example Question #12 : Graphing The Sine And Cosine Functions

In  , , and . To the nearest tenth, what is ?  A triangle with these characteristics cannot exist.   Explanation:

By the Law of Cosines: or, equivalently, Substitute:   ### All High School Math Resources 