Question

the sides of a triangle are 46, 44, and 82. use the pythagorean theorem to determine if 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: Calculate the square of each side

$$\begin{align*} 46^{2}&=2116\\ 44^{2}&=1936\\ 82^{2}&=6724 \end{align*}$$

Step2: Calculate the sum of the squares of the two shorter sides

$$2116 + 1936=4052$$

Step3: Compare the square of the longest side with the sum of the squares of the other two sides

Since \(6724>4052\) (i.e., \(82^{2}>46^{2}+44^{2}\))

Answer:

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