Question

tell whether a triangle with sides 3 cm, 6 cm, and 8 cm is acute, right or obtuse. right obtuse acute

Explanation:

Step1: Recall the Pythagorean - related rule

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

Step2: Identify \(a\), \(b\), and \(c\)

Let \(a = 3\), \(b = 6\), and \(c = 8\).

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

\(a^{2}=3^{2}=9\), \(b^{2}=6^{2}=36\), so \(a^{2}+b^{2}=9 + 36=45\). And \(c^{2}=8^{2}=64\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(45<64\) (i.e., \(a^{2}+b^{2}

Answer:

obtuse