Question

the sides of a triangle are 65, 75, and 95. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse. answer: the triangle is blank because the square of the largest side blank the sum of the squares of the other two sides.

Explanation:

Step1: Calculate the squares of the sides

Let \(a = 65\), \(b=72\), \(c = 97\) (assuming \(c\) is the largest side).
\(a^{2}=65^{2}=4225\), \(b^{2}=72^{2}=5184\), \(c^{2}=97^{2}=9409\)

Step2: Check the Pythagorean relationship

Calculate \(a^{2}+b^{2}\): \(4225 + 5184=9409\)
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(65^{2}+72^{2}=97^{2}\))

Answer:

The triangle is right - angled because the square of the largest side equals the sum of the squares of the other two sides.