Required information

A force $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ of magnitude $105$ lb is applied to member $\backslash ($ A C D E $\backslash ),$ which is supported by a frictionless pin at $\backslash ($ D $\backslash )$ and by the cable $\backslash ($ A B E $\backslash ).$ Because the cable passes over a small pulley at $\backslash ($ B $\backslash ),$ the tension may be assumed to be the same in portions $\backslash ($ A B $\backslash )$ and $\backslash ($ B E $\backslash )$ of the cable. Assume $\backslash (\backslash$mathrm$\{$a$\}=3\backslash$mathrm$\{$in$\}\backslash ).$

Determine the tension in the cable.

The tension in the cable is

lb$.$