$4.$ Key member in a windmill truss $(38$ points$)$

The mid$-$sized wind turbine shown below left is supported by a simple truss which can be considered two$-$dimensional as shown below left.

It is $30$ m tall, $4$ m wide at its base, $2$ m wide at $\backslash ($ D E $\backslash )$ and $\backslash ($ F G $\backslash ),$ and mostly symmetric.

The wind and weight of the turbine exert a force on point $\backslash ($ H $\backslash )$ with total magnitude $650$ N at a slope of $\backslash (5/12\backslash ).$

$($Aspect ratio is not to scale, with these dimensions it would be more slender.$)$

$($a$)$ Identify the zero$-$force mmebers in the truss, if any. $(7)$

$($b$)$ Calculate the reactions at rocker $\backslash ($ A $\backslash )$ and pin C$.(10)$

$($c$)$ Calculate the force in member $\backslash ($ D G $\backslash )$ in the tower shown on the left. Is it in compression or tension? $(12)$

$($d$)$ Suppose the mid$-$level diagonal brace is switched as shown on the right. How does the force in member $\backslash ($ E F $\backslash )$ on the right compare to the force in $\backslash ($ D G $\backslash )$ in the left tower? $(9)$