$3\mathrm{.}61$ A $30-lb$ vertical force $P$ is applied at $A$ to the bracket shown, which is held by

screws at $B$ and $C.($a$)$ Replace P with an equivalent force$-$couple system at $B.$

$($b$)$ Find the two horizontal forces at $B$ and $C$ that are equivalent to the couple

obtained in part $a.$