$(6$ points$)$ Difficulty $(4/5)$

A crate is hung by ropes attached to a steel ring. Assume that the center of gravity $($CG$)$ of the crate shown lies at its geometric center, and that ring A lies directly above the crate's

CG$.$ The top surface of the crate is horizontal, and ring A lies $40$ inches above it$.$ Other dimensions are given as:

$a=48in$

$b=47in$

$c=8\mathrm{.}4in$

A load cell measures the tension in rope AC to be $T_{AC}=169lb.$ Find the weight of the crate and the tension in the other two ropes.

$W_{\text{c}\text{r}\text{a}\text{t}\text{e}}=$

$T_{AB}=$

$T_{AD}=$

be sure to include units with your answers