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Calculate the sum of the squares of the two shorter sides. If this is less than the square of the remaining, third, side then the triangle is obtuse.

There are three possibilities - let the three sides of the triangle be A, B and C with C the longest side (that is C ≥ A and C ≥ B). Then, if:

  1. A2 + B2 > C2 the triangle is acute
  2. A2 + B2 = C2 the triangle is right angled
  3. A2 + B2 < C2 the triangle is obtuse
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Q: When is a triangle obtuse when lengths of sides are given?
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What are the lengths of the sides of an obtuse triangle?

The 3 sides have different lengths


What is a shape with no congruent sides and one of it's angles is obtuse?

An obtuse scalene triangle would fit the given description


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