SOLUTION: What type of triangle does 11,10 and 13 make

Question 723234: What type of triangle does 11,10 and 13 make
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
To begin with, I would call that triangle , meaning that the 3 sides have different lengths.
The triangle is also , meaning that all three angles are acute (smaller than a right angle).

How do I know? Here is how.
The largest angle is opposite the longest side, the one measuring 13.
(for triangles, longer side is opposite larger angle, and shorter side is opposite smaller angle.
According to the Pythagorean theorem, a right triangle with legs (the shorter sides) measuring 10 and 11 would have a hypotenuse (the longer side) measuring
=about 14.87
and would look like this
If side AB has a shorter measure, , then angle C must be smaller than a right angle.
And since A is the largest of the 3 angles, all three angles are smaller than a right angle:
I can calculate the angle measures as , , and using the law of cosines, but that is much more advanced math (and not a fun calculation either).
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