A pin$-$connected structure is supported and loaded as shown in the figure. Member ABCD is rigid and is horizontal before the load $P$ is applied. Bars $(1)$ and $(2)$ are made of steel, each having a cross$-$sectional area of $1\mathrm{.}25$ in$.{?}^2.$ The normal stress in the bar $(1)$ must be limited to $23$ksi. $a=57$ in$.,b=50$ in$.,c=21$ in$.,L_1=66$ in$.,L_2=142$ in$.,E=30000($for both bars$)$