Question

the sides of a triangle are 84, 77, and 55. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse. answer attempt 1 out of 2 the triangle is because the square of the largest side the sum of the squares of the other two sides.

Explanation:

Step1: Identify the largest side

The sides are 84, 77, 55. The largest side \(c = 84\), and the other two sides \(a = 77\), \(b = 55\).

Step2: Calculate the square of the largest side

\(c^{2}=84^{2}=7056\)

Step3: Calculate the sum of the squares of the other two sides

\(a^{2}+b^{2}=77^{2}+55^{2}=5929 + 3025=8954\)

Step4: Compare the values

Since \(c^{2}=7056\) and \(a^{2}+b^{2}=8954\), and \(c^{2}

Answer:

The triangle is acute because the square of the largest side is less than the sum of the squares of the other two sides.