Required information

The structure $\backslash ($ A B C D $\backslash )$ given in the following figure is designed to support a finite mass hanging from a cable, $\backslash ($ D F $\backslash ),$ attached to the structure at point $\backslash ($ D $\backslash ).$

where $\backslash ($ x$=2\mathrm{.}000\backslash$mathrm$\{$~m$\},$ y$=2\mathrm{.}500\backslash$mathrm$\{$~m$\}\backslash ),$ and $\backslash ($ z$=2\mathrm{.}500\backslash$mathrm$\{$~m$\}\backslash )$

The structure is mounted to the ground by a hinge at $\backslash ($ B $\backslash )$ and a roller at $\backslash ($ C $\backslash )$ and is also supported by a horizontal cable, $\backslash ($ A E $\backslash ),$ attached to the wall. The mass of the object hanging from cable $\backslash ($ D F $\backslash )$ is $196$ kg $.$ The tension in the support cable $\backslash ($ A E $\backslash )$ is $\backslash (1,900\backslash$mathrm$\{$~N$\}\backslash ).$ It is desired to determine the force that each individual member will experience under the given loading conditions in order to decide what type of material to use to build the structure.

Calculate the force in member $\backslash ($ A B $\backslash )$ of the truss.

The force in member $\backslash ($ A B $\backslash )$ of the truss is