Balancing the four masses $A,B,C,$ and D effectively reduces noise pollution in the environment. Masses C and D make angles of $90$ deg and $210$ deg respectively with B in the same sense. The planes containing B and C are $300$ mm apart. Masses A$,$ B$,$ C$,$ and $D$ can be assumed to be concentrated at radii of $360mm,480mm,240mm,$ and $300$ mm $,$ respectively. The masses B$,$ C and D are $15kg,25kg$ and $20$ kg respectively. Determine the mass A and its angular position. Also, find the position of planes A and D$.$