Is it a coincidence that both the Sun and the Moon look of same size from the Earth? The Sun is huge, when compared to the Moon. Despite the huge difference in their size and distance from Earth, is it purely coincidental that they both look almost the same from Earth?
The coincidence isn't so much that they appear very similar sizes from Earth, but that we are alive to see them at the point in time in which they appear very similar sizes.  The moon is slowly moving away from the Earth, and at some point in the future the moon will be unable to totally eclipse the sun and conversely, if you could step far into prehistory, you would be able to see the moon with a much greater angular diameter than you see it now.

Most research I've found on the topic seem to be unavailable through my institute, however I did find one paper, "Outcomes of tidal evolution", which references results from Goldreich's research on the subject.


  This qualitative description of the eventual disruption of the Earth-Moon system is confirmed by the results of Goldreich's numerical integration, which showed that the moon will recede to 75 Earth radii, when spin-orbit synchronism will be reached; then the Moon's orbit will decay steadily inward because of the influence of the Sun.


For reference, the Moon is currently at a distance of approximately 60.3 Earth radii.  As such, the moon will steadily move away until synchronism would be reached, and from that point begin to recede towards the Earth due to the tidal affects of the Sun on the Earth disturbing the synchronization. It would seem that at some eventual point in the far distant future, it will return to this coincidental position once again.


  Counselman III, Charles C. "Outcomes of tidal evolution." The Astrophysical Journal 180 (1973): 307-316.