SUGGESTION FOR TRIANGLES PROBLEM

A suggestion for this problem: instead of trying to know angles and something like that, you can use the area formula for triangles in which you only need to know 3 sides (Heron's Formula) https://i.ytimg.com/vi/6c_VZQhIwCk/maxresdefault.jpg. You can calculate the area for the 3 sides and, if the result is a complex number, you can assure that those 3 lenghts do not form a triangle.