Question

the lengths of a triangle are given below. is the the triangle obtuse, acute, or right? 4, 5, 6

Explanation:

Step1: Calculate the sum of squares of the two shorter sides

Let \(a = 4\), \(b = 5\), \(c = 6\). The two shorter sides are \(a\) and \(b\).
\(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25=41\)

Step2: Calculate the square of the longest side

\(c^{2}=6^{2}=36\)

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

If \(a^{2}+b^{2}>c^{2}\), the triangle is acute. If \(a^{2}+b^{2}=c^{2}\), the triangle is right - angled. If \(a^{2}+b^{2}Since \(41>36\) (i.e., \(a^{2}+b^{2}>c^{2}\))

Answer:

acute