Q$3.$ A $7-$m boom is held by a ball and socket at $\backslash ($ A $\backslash )$ and by two cables $\backslash ($ E B F $\backslash )$ and $\backslash ($ D C $\backslash )$; cable $\backslash ($ E B F $\backslash )$ passes around a frictionless hook at $\backslash ($ B $\backslash ).$ A load is acting downward and having a magnitude of $\backslash (3.\backslash$boldsymbol$\{$x$\}\backslash$mathrm$\{$kN$\}\backslash ),$ where $\backslash (\backslash$boldsymbol$\{$x$\}\backslash )$ is the last digit of your student number $($e$.$g$.$ the load is $3\mathrm{.}8$ kN if your number is $12345678$A$).($a$)$ Draw free$-$body diagram of the boom. $($b$)$ Determine the tensions in the two cables.

$[10$ marks$]$