The configuration shown is for the problems below. Solid part BCD can pivot about point $C.$ The part $AB$ can extend $($it represents a hydraulic cylinder$).$ One end is fixed at point A $,$ and the other end is attached to point B$.$

$[$I have done part a and b; just need help with c and d$.$ The answer for pt a: theta $=7\mathrm{.}181$ degrees, part b: B moves $75\mathrm{.}003$mm to the right and $4\mathrm{.}706$ mm down$]$

$($c$)$ Given that the point B moves $75$ mm to the right and $4\mathrm{.}70$ mm downward, by how much has AB changed length? By how much has AB rotated $($Answers: $64\mathrm{.}7mm,5\mathrm{.}75$ degrees $)$

Hint: it is hard to find the angle of rotation of AB directly; it is easier to find the angle that AB makes with the horizontal $($or vertical$)$ before and after rotation and subtract.

$($d$)$ Determine the maximum length that hydraulic cylinder AB can reach. Show how you can predict theoretically the maximum length of AB$,$ and the angle of CD at which AB reaches its max length.