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Problem A $(50$ points$)$

A system of two inextensible, flexible cables supports a uniform platform in a horizontal position, which in turn supports two pieces of equipment at the locations shown in the diagram below. A concentrated $0\mathrm{.}5$ kN vertical load is applied at $\backslash ($ B $\backslash ).$ The platform weighs $1$ kN and the pieces of equipment weigh $\backslash ($ W$\_\{1\}=0\mathrm{.}25\backslash$mathrm$\{$kN$\}\backslash )$ and $\backslash ($ W$\_\{2\}=0\mathrm{.}75\backslash$mathrm$\{$kN$\}\backslash ).$ The cables have negligible weight. Determine a$)$ the inclination and length of each of the three cable segments $\backslash ($ A B$,$ B C $\backslash )$ and $\backslash ($ D E $\backslash )$ that will maintain the platform in the position shown, and b$)$ the tension in each of the three cable segments.