given the lengths of a side of a triangle identify the triangle as acute, right, or obtuse
1 A triangle with all interior angles measuring less than 90Â° is an acute triangle or acute-angled triangle. 2  If c is the length of the longest side, then, where a and b are the lengths of the other sides. 3  A triangle with one interior angle measuring more than 90Â° is an obtuse triangle or obtuse-angled triangle. If the legs of a right triangle have the same length, then the angles opposite those legs have the same measure. 2  Since these angles are complementary, it follows that each measures 45 degrees. 3  By the Pythagorean theorem, the length of the hypotenuse is the length of a leg times â2.