Question

the lengths of a triangle are given below. is the the triangle obtuse, acute, or r 11, 12, 15

Explanation:

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

Let \(a = 11\), \(b=12\), \(c = 15\) (where \(c\) is the longest side). Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=11^{2}+12^{2}=121 + 144=265\)

Step2: Calculate the square of the longest side

Calculate \(c^{2}\):
\(c^{2}=15^{2}=225\)

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 \(265>225\) (i.e., \(a^{2}+b^{2}>c^{2}\))

Answer:

acute