Here's the problem. The red lines in the following photo are the identical number of pixels long according to MS Paint:
That problem has its roots here:
The 200x200 dimensions are incorrect. The op used the height of the movable crane not the derrick.
The different angles of the 2 pics make comparisons of height to width ratios inaccurate.
In the closeup you are looking up at the rig and in the distant shot it is basically an elevation.
In the closeup the crane appears taller than the derrick but in reality it isn't. The cranes are just closer.
If you're going to compare the 2 images you need to keep "measurements" from the closeup to a single plane, ie the front of the platform. It's also best to use ratios as you can't get actual measurements from the closeup view because perspective plays a part.
One third of the platform is the legs.
My compliments to the OP for at least doing an actual experiment, a rarity here.
However, you forgot to include refraction in your calculations. The amount hidden with refraction considered is 54.5 feet.
Can you post your original image for us to look at?