A triangle in which all three angles are acute angles. A triangle which is neither acute nor a right triangle (i.e., it has an obtuse angle) is called an obtuse triangle. 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 acute, cos C>0. Therefore, an acute triangle satisfies a^2 + b^2>c^2, b^2 + c^2>a^2, and c^2 + a^2>b^2. The smallest number of acute triangles into which an arbitrary obtuse triangle can be dissected is seven if B>90°, B - A, B - C<90°, and otherwise eight. A square can be dissected into as few as 9 acute triangles.

obtuse triangle | Ono inequality | right triangle