Law of cosines problem

Question

I need to prove the following statement:

Use the law of cosines to justify the statement that if a, b, and  c are the sides of triangle ABC and a<b<c, then ABC is acute if a² + b² > c² and obtuse if a² + b² < c²

Answer 1

The law of cosines is:

We can rearrange the terms:

If a² + b² > c^2, then the numerator of the right side is negative, so cos C is positive, and C is acute.

If a² + b² < c² cos C is negative and C is obtuse.