Question

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

4, 5, 7
5, 7, 8
6, 7, 10
7, 9, 12

Answer 1

B 5,7,8

Explanation:

Answer 2

There are several ways you can answer this. The law of cosines may be helpful. It tells you

... c² = a² + b² - 2ab·cos(C)

or

... cos(C) = (a² + b² - c²)/(2ab)

If this value is negative, then angle C is obtuse. Since 2ab is always positive, it amounts to finding the sign of

... a² + b² - c²

Of course, for repetitive calculations, a spreasheet or other machine evaluator is helpful.

The results shown in the figure indicate that side lengths {5, 7, 8} result in an acute triangle.