Question

determine whether the set of lengths forms a right, acute, or obtuse triangle. 14 in., 16 in., 20 in.

Explanation:

Step1: Identify the longest side

The longest side \( c = 20\) in. Let \( a = 14\) in and \( b = 16\) in.

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

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$$ c^{2}=20^{2}=400 $$

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=452>c^{2} = 400\) (i.e., \(a^{2}+b^{2}>c^{2}\) where \(c\) is the longest side)

Answer:

The triangle is acute.