Finding Angles with Trigonometry

The figure referenced is below:

By the Law of Cosines, the relationship of the measure of an angle of a triangle and the three side lengths , , and , the sidelength opposite the aforementioned angle, is as follows:

All three side lengths are known, so we are solving for . Setting

, the length of the side opposite the unknown angle;

;

;

and ,

We get the equation

Solving for :

Taking the inverse cosine:

,

the correct response.