Question

the sides of a triangle are 79, 40, and 64. 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 79, 40, and 64. The largest side $c = 79$, and the other two sides $a = 40$, $b = 64$.

Step2: Calculate the square of the largest side

$c^{2}=79^{2}=6241$.

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

$a^{2}+b^{2}=40^{2}+64^{2}=1600 + 4096=5696$.

Step4: Compare the two results

Since $c^{2}=6241$ and $a^{2}+b^{2}=5696$, and $c^{2}>a^{2}+b^{2}$.

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.