Question

the sides of a triangle are shown. determine if the triangle is an acute, right or obtuse triangle. 16, 18, 24

Explanation:

Step1: Identify the longest side

Let \(a = 16\), \(b = 18\), \(c=24\) (where \(c\) is the longest side).

Step2: Apply the Pythagorean - related inequalities

Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\(a^{2}+b^{2}=16^{2}+18^{2}=256 + 324=580\).
\(c^{2}=24^{2}=576\).

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

Since \(a^{2}+b^{2}=580>c^{2}=576\), the triangle is acute.

Answer:

The triangle is acute.