Difficult Trig/Geometry Problem

[jbarker2160]

If the blue figures are all rectangles arranged as shown, given values for A, B and W, how would you calculate C and Ɵ?

 

[metastable]

I suspect the way it’s depicted, C could be any length.

 

[jbarker2160]

I suspect the way it’s depicted, C could be any length.

You're right. C would be expressed as an inequality.

 

[JayJay]

It seems we should assume that:
The top four corners of the uprights and the leftmost corner of the diagonal are co-linear
The bottom four corners of the uprights and the rightmost corner of the diagonal are co-linear
Could jbarker2016 confirm this and show their work / thoughts so far.

 

[jbarker2160]

It seems we should assume that:
The top four corners of the uprights and the leftmost corner of the diagonal are co-linear
The bottom four corners of the uprights and the rightmost corner of the diagonal are co-linear
Could jbarker2016 confirm this and show their work / thoughts so far.

The co-linearity of the points is only useful for establishing a minimum value for C, but in the drawing that's the case.

I've already tried by using every given dimension and combination thereof (tan(theta)=B/A, tan(theta)=B/(A-W), tan(theta)=B/(A-2W), etc.) but none of those give the correct answer. It seems like the answer will be something like B/sin(theta)=sqrt((A-x)²+B²) where x is the distance between the upper-left-most point of the leftmost upright and the leftmost point of the diagonal) but that leaves multiple unknowns and I'm unsure of where to go from there.