Question $3(25$ points$)$ Two traffic signals are suspended to the position shown by cables AB $,BC,$ and $CD.$ The force in cable $AB$ is $10-1b,$ and the force in cable $CD$ is $20-1b.$

a$)$ Determine the force in cable BC$.$

b$)$ Determine the weight of traffic signal at $B.$

c$)$ Determine the weight of traffic signal at $C.$

d$)$ Determine the angle $.$