Not as much as you would expect given the size of the sun.
Sorry, you lost me. I expected half a degree based on the angular size of the sun in the sky earlier in this thread. The size of the sun over the distance to earth happens to work out to an angle of half a degree - that's all there is to it.
A quick calculation shows that a B747 will cover half a degree at 5000ft, which means at least up to that altitude it will cast a noticeable shadow.
No, it means that if only ray optics is relevant, there is a (gradually shrinking) shadow generated which vanishes at 5000 ft. It's an upper limit, because both wave diffraction and scattering on air will further decrease your shaded region. Also, the 747 is not a disc, and having only a small patch of sun uncovered is enough to remove a shadow.
In actual reality, the shadow will be gone somewhat before that altitude, though it's hard to say for sure when exactly.
Note that a good part of the effect of haze and air scattering is however accounted for by counting direct (diffuse and specular) and indirect (ambient) light - the depth of a shadow depends on the strength of ambient light over diffuse light, which in turn depends on haze (often that is Rayleigh light, which is why shadows are somewhat blue on a clear day). So there's only a specific scattering channel (mostly Mie scattering of rays just missing the airplane into the shadow cone) which tends to remove the shadow specifically as a function of distance.
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