Thanks, Plas. I was beginning to think I was in a minority of 1. I've been assuming that by "shadow", umbra is intended. Now if we substitute discs for the plane and the bird, we could put the 12ft disc on the ground and it would obviously create a 12ft shadow! Without doing any calculations, I suspect that the 120ft disc would not have to be that high (certainly not as high as being suggested) to create a 12ft shadow. In fact, 120ft is miniscule compared to the diameter of the sun and I don't think such a disc would have to be particularly high to go antumbral (ie create an annular eclipse). But I'm open to persuasion by numbers.
(I'm taking the sun to be overhead and light scattering to be nil)