$7$

The structure consisting of bars $\backslash ($ A C D $\backslash )$ and $\backslash ($ B C $\backslash )$ connected by a pin at $\backslash ($ C $\backslash )$ is supported by pins at $\backslash ($ A $\backslash )$ and B$.$ A counterclockwise couple of magnitude $\backslash (200\backslash$mathrm$\{$kN$\}-\backslash$mathrm$\{$m$\}\backslash )$ is applied at point A as shown. A force of magnitude $\backslash (80-\backslash$mathrm$\{$kN$\}\backslash )$ is to be applied at the end D of bar ACD $.$ What should be the value of the angle beta for the magnitude of the reaction at pin B to be maximum? $($Assume that the bars are of negligible weight.$)$ Write your answer and reasoning $*$