Question

the sides of a triangle are 42, 15, and 39. 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 42, 15, 39. The largest side is 42.

Step2: Calculate the square of the largest side

$42^{2}=1764$

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

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

Step4: Compare the two values

Since $1764>1746$ (i.e., the square of the largest side is greater than the sum of the squares of the other two sides), the triangle is obtuse.

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.