Question

the sides of a triangle are 89, 77, and 59. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
answer
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 89, 77, 59. The largest side is 89.

Step2: Calculate the square of the largest side

$89^{2}=7921$.

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

$77^{2}+59^{2}=5929 + 3481=9410$.

Step4: Compare the two values

Since $7921<9410$ (i.e., the square of the largest side is less than the sum of the squares of the other two sides), the triangle is acute.

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.