Question $4.$

$[20$ Marks$]$

$($a$)$ Consider the complex shape below and find the centroid, with free body diagram $($Break each component$)$

$[10$ marks$]$

Figure Q$4$a

$($b$)$ If the coordinate direction angles for $F3$ are $3=120$ o$,3=60$ o and $3=45$ o$,$ determine the magnitude and coordinate direction angles of the resultant force acting on the eyebolt, shown in Figure Q$4$b$.$

$[10$ marks$]$ Hint: Represent all forces and the resultant in the cartesian vector form.