Question

the sides of a triangle are 15, 39, and 40. 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 15, 39, 40. The largest side $c = 40$. The other two sides are $a = 15$ and $b = 39$.

Step2: Calculate the square of the largest side

$c^{2}=40^{2}=1600$.

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

$a^{2}+b^{2}=15^{2}+39^{2}=225 + 1521=1746$.

Step4: Compare the values

Since $c^{2}=1600$ and $a^{2}+b^{2}=1746$, 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.