Question

the sides of a triangle are 67, 75, and 35. 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

The sides are 67, 75, and 35. The largest side $c = 75$, and the other two sides $a = 67$ and $b = 35$.

Step2: Calculate the square of the largest side

$c^{2}=75^{2}=5625$.

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

$a^{2}+b^{2}=67^{2}+35^{2}=4489 + 1225=5714$.

Step4: Compare the values

Since $c^{2}=5625$ and $a^{2}+b^{2}=5714$, 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.