Question

question
the sides of a triangle are 91, 61, and 69. 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 and calculate its square

The largest side is 91. Its square is $91^{2}=8281$.

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

The other two sides are 61 and 69. Their squares are $61^{2}=3721$ and $69^{2}=4761$. The sum is $3721 + 4761=8482$.

Step3: Compare the two - values

Since $8281<8482$ (square of the largest side is less than the sum of the squares of the other two sides). According to the Pythagorean - related rules for triangles, if $c$ is the longest side of a triangle and $a$ and $b$ are the other two sides, when $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.