Question

the sides of a triangle have lengths 3, 4, and 4. what kind of triangle is it? acute right obtuse

Explanation:

Step1: Recall the triangle - type determination rule

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), if \(a^{2}+b^{2}=c^{2}\), it is a right - triangle; if \(a^{2}+b^{2}>c^{2}\), it is an acute - triangle; if \(a^{2}+b^{2}

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

Calculate \(a^{2}+b^{2}\): \(3^{2}+4^{2}=9 + 16=25\). Calculate \(c^{2}\): \(4^{2}=16\).

Step3: Compare the values

Since \(25>16\), that is \(a^{2}+b^{2}>c^{2}\), the triangle is acute.

Answer:

acute