Question

the sides of a triangle are 27, 17, and 13. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
answer attempt 1 out of 2
the triangle is dropdown because the square of the largest side the sum of the squares of the other sides.
options in dropdown: obtuse, right, acute

Explanation:

Step1: Identify largest side

Largest side is 27. Calculate \(27^2 = 729\).

Step2: Calculate sum of squares of other sides

Other sides: 17 and 13. \(17^2 + 13^2 = 289 + 169 = 458\).

Step3: Compare values

Since \(729 > 458\) (square of largest side > sum of squares of others), by the Pythagorean inequality theorem, the triangle is obtuse.

Answer:

obtuse