SOLUTION: If you have three side lengths and you know they can make a triangle how can you figure out if the triangle will be obtuse, acute, or right triangle by just using the lengths?

Algebra ->  Triangles -> SOLUTION: If you have three side lengths and you know they can make a triangle how can you figure out if the triangle will be obtuse, acute, or right triangle by just using the lengths?       Log On


   

Question 969951: If you have three side lengths and you know they can make a triangle how can you figure out if the triangle will be obtuse, acute, or right triangle by just using the lengths?
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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Let a and b be the two shorter lengths and let c be the longest length.
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If a%5E2%2Bb%5E2=c%5E2 then it is a right triangle.
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If a%5E2%2Bb%5E2%3Ec%5E2 then it is an acute triangle.
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If a%5E2%2Bb%5E2%3Cc%5E2 then it is an obtuse triangle.
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If a=b, it is an obtuse isosceles triangle.
If a or b=c, it is an acute isosceles triangle.
If a=b=c, it is an equilateral triangle.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagorean Theorem formula. If truth for any combination of sides, then this is a right triangle.

Best way to arrange the numbers for the sides is to use the longest side length for one member of the equation and the other two side lengths for the other member. The hypotenuse of a right triangle is the triangle's longest side. If longest side squared is greater than sum of squares of the other two sides, then this triangle has an obtuse angle.