Please help, show all work and round to $3$ significant figures.

A crate weighs $585$ lb and is hung by three ropes attached to a steel ring at A such that the top surface is parallel to the $xy$ plane. Point $A$ is located at a height of $h=31$ in above the top of the crate directly over the geometric center of the top surface. Use the dimensions given in the table below to determine the tension in each of the three ropes.

$2013$ Michael Swanbom

Values for dimensions on the figure are given in the following table. Note the figure may not be to scale.

$\backslash$table$[[$Variable$,$Value$],[a,48$ in$],[b,29$ in$],[c,13\mathrm{.}2$ in$]]$

The tension in rope $AB$ is lb

The tension in rope $AC$ is lb

The tension in rope $AD$ is lb