use the pythagorean inequality theorem
The sides of a triangle have lengths 3, 33, and 32. What kind of triangle is it?
a. acute b. right c. obtuse
To determine what kind of triangle it is, we can check if the Pythagorean inequality theorem holds true for these side lengths.
The Pythagorean inequality theorem states that the sum of the squares of the two shorter sides of a triangle must be greater than the square of the longest side.
In this case, the squares of the side lengths are:
$3^2 = 9$, $32^2 = 1024$, and $33^2 = 1089$
Adding the squares of the two shorter sides, we get $9 + 1024 = 1033$.
Since 1033 is less than 1089, which is the square of the longest side, the Pythagorean inequality theorem is not satisfied.
Therefore, this triangle is an obtuse triangle.