SOLUTION: explain in a paragraph how, given the lengths of three sides of a triangle, you can determine whether the triangle is right triangle or not.

Question 586899: explain in a paragraph how, given the lengths of three sides of a triangle, you can determine whether the triangle is right triangle or not.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If the squares of the lengths of the two shorter sides add up to exactly the square of the length of the longer side, it is a right triangle. Otherwise the triangle is not a right triangle. If the square of the length of the longer side is greater than the sum of the squares of the lengths of the two shorter sides, the triangle is obtuse, and if the square of the length of the longer side is lesser than the sum of the squares of the lengths of the two shorter sides, the triangle is acute.
EXAMPLES:
A triangle with sides measuring 3, 4, and 5 is a right triangle because .
A triangle with sides' lengths 3, 4, and 6 is not a right triangle because . (It's an obtuse triangle).
A triangle with sides measuring 8, 15, and 17 is a right triangle because .
A triangle with sides' lengths 8, 15, and 16 is not a right triangle because . (It's an acute triangle).
FURTHER EXPLANATIONS:
If the square of the length of the longer side is greater than the sum of the squares of the lengths of the two shorter sides, the longer side is longer than it would be if it were opposed to a right angle, and the angle it opposes is greater than a right angle, making the triangle obtuse. If the square of the length of the longer side is lesser than the sum of the squares of the lengths of the two shorter sides, the longer side opposes an angle that�s smaller than a right angle, while larger than the angles opposed to the shorter sides, so all angles are acute, and it is an acute triangle.
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