For the structure $($three hinged frame$)$ shown below subject to a factored distributed load $\backslash (2\backslash$mathrm$\{$k$\}/\backslash$mathrm$\{$ft$\}\backslash ),$ it is required to:

Note that all connections are pinned.

$($a$)$ Show that the force in member BC is $20$ kips.

$($b$)$ Design member BC as a $2-$angles back$-$to$-$back. Assume Fy $=50$ ksi $.$

$($c$)$ Redesign member BC as a single angle.

$($d$)$ Which of the two designs is more economic?