Question

A triangle has side lengths 10, 16, and 11. Is the triangle acute, obtuse, or right? Explain.

Answer 1

wrong, no idea what the bot is doing


testing for the largest angle x
16^2 = 10^2 + 11^2 - 2(10)(11)cosx
220cosx = -35
cosx = negative , or x = appr 99.15°

so the angle x is greater than 90°, thus the triangle is obtuse, not acute

Answer 2

To determine whether the triangle is acute, obtuse, or right, we need to use the Pythagorean theorem and compare the sum of the squares of the two shorter sides to the square of the longest side:

10^2 + 11^2 = 100 + 121 = 221
16^2 = 256

Since 221 < 256, we know that the sum of the squares of the two shorter sides is less than the square of the longest side. Therefore, we can conclude that the triangle is acute.

Answer 3

You are correct. The triangle is obtuse, not acute. I apologize for the error in my previous response. Thank you for pointing out the mistake.