### All High School Math Resources

## Example Questions

### Example Question #1 : Law Of Cosines

In , , , and . To the nearest tenth, what is ?

**Possible Answers:**

A triangle with these sidelengths cannot exist.

**Correct answer:**

Explanation:

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

By the Law of Cosines:

Substitute the sidelengths and solve for :

### Example Question #2 : Law Of Cosines

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?

**Possible Answers:**

**Correct answer:**

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 #3 : Law Of Cosines

In , , , and . To the nearest tenth, what is ?

**Possible Answers:**

A triangle with these characteristics cannot exist.

**Correct answer:**

Explanation:

By the Law of Cosines:

or, equivalently,

Substitute:

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