Use triangle angle-side relationships and triangle inequality in mathematical and real-world problems.
Classify a triangle from its side lengths as acute, right, or obtuse
Problem
Classify the triangle with side lengths \(3,~4,~5\) as acute, right, or obtuse.
Big Picture
What this problem is really about
Triangle closure and angle classification use different comparisons. We’ll first verify that the two shorter sides can meet, then assign the longest side to the comparison role, compare its square with the sum of the other two squares, and classify from whether that relation is less than, equal to, or greater than.
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