A triangle has side lengths 10, 16, and 11. Is the triangle acute, obtuse, or right? Explain.
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.
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
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.
To determine if the triangle is acute, obtuse, or right, we need to analyze the relationship between the square of the longest side and the sum of the squares of the other two sides.
First, we need to determine which side of the triangle is the longest. By comparing the given side lengths, we see that 16 is the longest side.
Now, we can determine if the triangle is acute, obtuse, or right by using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
So, let's find the squares of the side lengths:
10^2 = 100
11^2 = 121
16^2 = 256
Now, we compare the sum of the squares of the two shorter sides to the square of the longest side:
100 + 121 = 221
Since 221 is less than 256, we can conclude that the given triangle is an acute triangle.
In summary, the triangle with side lengths 10, 16, and 11 is an acute triangle.