Question

the sides of a triangle are 60, 77, 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 60, 77, and 64. The largest side $c = 77$, and the other two sides $a = 60$ and $b = 64$.

Step2: Calculate the square of the largest side

$c^{2}=77^{2}=5929$.

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

$a^{2}+b^{2}=60^{2}+64^{2}=3600 + 4096=7696$.

Step4: Compare the two values

Since $c^{2}=5929$ and $a^{2}+b^{2}=7696$, 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.