SOLUTION: Using pythagorean inequalities what are the classification of the following triangles? 15,36,39. 9,17,14. 15,13,18.

Question 827908: Using pythagorean inequalities what are the classification of the following triangles? 15,36,39. 9,17,14. 15,13,18.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
so
a triangle with sides measuring 15, 36, and 39 is a right triangle.

so
a triangle with sides measuring 9, 14, and 17 is an obtuse triangle.
In a right triangle with legs measuring 9 and 14, the square of the length of the longest side would be 277.
In this triangle the square of the length of the longest side is greater, so the longest side is longer than it would be for a right triangle, and the angle opposite the longest side is larger than a right angle.

so
a triangle with sides measuring 13, 15, and 18 is an acute triangle.
In a right triangle with legs measuring 13 and 15, the square of the length of the longest side would be 394.
The longest side in this triangle is shorter than that, and that means the angle opposite that side is smaller than a right angle.
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