Knowing that the tension in cable $AD$ is $180$ lb $,$ determine

$($a$)$ the angle between cable $AD$ and the boom $AB,$

$($b$)$ the projection on $AB$ of the force exerted by cable $AD$ at point $A.$

$($c$)$ the moment of the tension in cable $AD$ about $B.$

$($d$)$ the moment of the tension in cable $AD$ about $BA.$

$($e$)$ the moment of the tension in cable $AD$ about $x$ axis.

$($f$)$ the moment of the tension in cable $AD$ about $y$ axis.

$(g)$ the moment of the tension in cable $AD$ about $z$ axis.