1. The problem statement, all variables and given/known data The base b and the area k of a triangle are fixed. Determine the base angles if the angle at the vertex opposite b is to be a maximum. 2. Relevant equations 3. The attempt at a solution The answer the book gives is arctan(4k/b2) I looked at the solution to the Regiomontanus' angle maximization problem but I could not modify some part of the solution to get this. Also I tried to put everything in terms of h and b.(ie. if k and b are constant, h(height) also must be constant. So all the triangles we get with different angles are constructed if you put a base on a line and put a point on the paper such that when you connect the lines to the edge of the base to the point the required constant area should be achieved. Then just move the point in a line parallel to the base. Then becomes clear from a qualitative viewpoint(not rigorous) that the maximum angle should be there when the point intersects the altitude of the base. But still how do I get this base angle.(Use lagrange's multipliers to help or just traditional calculus)?