Compare the lengths of the sides by the one simple rule that applies to all triangles. The length of any one side must be between zero and the sum of the other two sides. Assuming that all the lengths are greater than zero, the only side you really need to test is the longest side. If the longest side is less than the sum of the lengths of the other two sides, the triangle is possible -- assuming that there are no other constraints on the shape of the triangle.
Use the Pythagorean theorem to check the lengths of the sides of a triangle. If A and B are the two shortest sides of the triangle and C is the longest side, we must have C^2 = A^2 + B^2. If this relationship does not hold, the three sides may still be the sides of a triangle, but it will not be a right triangle. In right triangles, one angle is a right angle -- 90 degrees -- and the longest side is directly across from the right angle.
Apply the law of sines when the angles are known. If the angles are all positive and add up to 90 degrees, a triangle is possible and the ratio of the lengths are determined by the ratios of the angles, but the triangle could be of any size. Once one side is determined, the other two sides are determined by the relationship a / Sin A = b / Sin B = c / Sin C, where "a" is the side across from angle A, "b" is the side across from angle B and "c" is the side across from angle C.