SOLUTION: The sides of a triangle measure 4, 9, and 11. Is this a right triangle? If not then is it acute or obtuse?

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Question 1209390: The sides of a triangle measure 4, 9, and 11. Is this a right triangle? If not then is it acute or obtuse?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

We use the Converse of the Pythagorean Theorem.
Here are the three possibilities:
  • If a%5E2%2Bb%5E2+=+c%5E2 then it's a right triangle.
  • If a%5E2%2Bb%5E2+%3E+c%5E2 then the triangle is acute.
  • If a%5E2%2Bb%5E2+%3C+c%5E2 then the triangle is obtuse.
a,b,c are the sides of the triangle.
c is always the longest side. The a,b can be in any order.

a = 4, b = 9, c = 11 are the three sides
a%5E2%2Bb%5E2+=+4%5E2%2B9%5E2+=+16%2B81+=+97
c%5E2+=+11%5E2+=+121

In short,
a%5E2%2Bb%5E2+=+97
c%5E2+=+121

The results 97 and 121 aren't equal, so the a%5E2%2Bb%5E2+=+c%5E2 case is false.
This is not a right triangle.
The result of a%5E2%2Bb%5E2 is smaller than the result of c%5E2 (since 97 < 121) so we conclude that a%5E2%2Bb%5E2+%3C+c%5E2 is case.
The triangle is obtuse.

You can confirm this using an online tool such as this one or you can use GeoGebra (the GeoGebra link may take a bit of time to load).
There are many other similar online tools.

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Answer: Obtuse