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.
