You might be able to just survey the thing. If you’ve got a good floor plan and can borrow some surveying equipment, you should be able to take angles to the top and just work out the height that way. Your best bet would probably be to use averaged GPS measurements, or existing surveys, to get an accurate horizontal distance to the spire, then take the angle from the base to the spire and work out some trig. You might be able to get away with just a plain camera, if you can correct for the lens distortion.
This is probably the best way to actually figure out the actual height of the Shard (if one can properly figure out whether the Shard has a well-defined and level base).
You might be able to just survey the thing. If you’ve got a good floor plan and can borrow some surveying equipment, you should be able to take angles to the top and just work out the height that way. Your best bet would probably be to use averaged GPS measurements, or existing surveys, to get an accurate horizontal distance to the spire, then take the angle from the base to the spire and work out some trig. You might be able to get away with just a plain camera, if you can correct for the lens distortion.
This is probably the best way to actually figure out the actual height of the Shard (if one can properly figure out whether the Shard has a well-defined and level base).