Triangle the hypotenuse equals the sum of the squares of the lengths of the two other sides. If the hypotenuse has length "c", and the legs have lengths "a" and "b", then the theorem states that The converse is true: if the lengths of the sides of a triangle satisfy the above equation, then the triangle has a right angle opposite side "c". Some other facts about right triangles: For all triangles, angles and sides are related by the law of cosines and law of sines (also called the "cosine rule" and "sine rule"). The triangle inequality states that the sum
Triangle inequality that the longest side length is less than the semiperimeter. A mathematically equivalent formulation is that the area of a triangle with sides "a", "b", "c" must be a real number greater than zero. Heron's formula for the area is In terms of either area expression, the triangle inequality imposed on all sides is equivalent to the condition that the expression under the square root sign be real and greater than zero (so the area expression is real and greater than zero). The triangle inequality provides two more interesting constraints for triangles whose sides are "a, b, c", where "a