High School Math : Applying the Law of Cosines

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Applying The 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 : Applying The 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 : Applying The 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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