An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A triangle must be either obtuse, acute, or right. From the law of cosines, for a triangle with side lengths a, b, and c, cos C = (a^2 + b^2 - c^2)/(2a b), with C the angle opposite side C. For an angle to be obtuse, cos C<0. Therefore, an obtuse triangle satisfies one of a^2 + b^2

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