a$)$ Determine the tension in cables $AB,AD,$ and AC if the weight of the signal light is $500$ N $,$

b$)$ Determine the moment of $T_{BA}$ about point $E,$ the moment of $T_{CA}$ about point $F,$ and the moment of $T_{DA}$ about point G $,$ and

c$)$ Find the perpendicular distances from $E$ to $AB,F$ to $AC,$ and $G$ to $AD.$