(c) 5/29/06 Ian Williams Goddard
A popular conspiracy theory promoted by numerous websites, books, and videos holds that on September 11, the Pentagon was struck not by Flight 77 but by some other object, perhaps a missile. This report examines both the primary argumentation and empirical data used to support that theory. Let us first examine the fundamental argument underlying the theory, which is expressed in the following contrary argument:
Each counter example satisfies the falsification criterion by showing that a hole smashed into a stone-walled building (like the Pentagon) by an aircraft can be smaller than the aircraft's wing span. So the fundamental argument for the "no Boeing 757" theory is falsified under empirical testing in a domain including historic precedent showing what happens when large aircraft impact large stone-walled buildings. Indeed, the given outcomes are probably the rule: wings will tend to be shorn off when impacting a more solid stone wall while the fuselage having much more mass and thus momentum would exceed the wall's strength.
Evidence of Wing Imapct
If the wings of Flight 77 were demolished upon striking the stone wall of the Pentagon, then one would expect some evidence of their impact against the exterior wall as well as evidence of their destruction on the outside. Indeed, such evidence is at hand...
The next images zoom in on both sides of the impact hole (buried under the collapse) where we can see evidence that the wings of Flight 77 slammed into the wall:
The left-hand photo shows that to the left of the impact hole the exterior stone facade along the first floor was knocked off the underlying bricks. This would be where the left wing struck. While the stone facade was blasted off, the windows sustained surprisingly little damage because the Pentagon had been reinforced to withstand being bombed. The right-hand photo shows damage to the right of the impact hole where a linear pattern of maximal impact damage is seen, as indicated by the animated red line. The American Society of Civil Engineers (ASCE) report attributes that damage to impact by the right wing. 
The photos above suggest that the length of damage caused by the right wing was less than that caused by the left wing. An explanation for this discrepancy might be found in the account of an eyewitness. The ASCE report cites the eyewitness account of Frank Probst, who was outside working on a Pentagon renovation project taking place at the time. As he stepped out of a construction trailer he saw Flight 77 approaching, whereupon he "hit the ground and observed the right wing tip pass through the portable 750 kW generator."  It's possible that such an impact damaged the right wing and thereby blunted the extent of its impact against the wall.
Additionally, the ASCE report notes that Probst observed "pieces of wing debris" fall around him outside the Pentagon.  Wing debris falling around someone outside the Pentagon indicates that the wings were fragmented outside the Pentagon. And finally, fragmented aircraft debris can also seen scattered all over outside the Pentagon here.
Those who advance the argument that the impact hole in the Pentagon was too small for a Boeing 757 seem to assume that commercial aircraft are solid steel objects impervious to crash-induced deformation and fragmentation. That indestructibility assumption expresses ignorance of the fact that the aluminum skin of commercial jets is less than an inch thick. As such, commercial jets are more like large tin cans than solid steel objects -- so long as they don't explode or smash into stone-walled buildings, their structural integrity is suitable for their intended task of aerial transportation.
From a stand point of good analysis, what is most disturbing about the given theory is how much its believers are willing to allow to become inexplicable by accepting its flawed argument falsified above. A good theory explains circumstances, but this theory makes them more inexplicable. For example, if Flight 77 did not hit the Pentagon, then what became of Flight 77 and its passengers? Moreover, why would anyone who wanted the disaster to happen plan to fake Flight 77 crashing and thereby in addition to having to hide their role in that crime also have to manage two complex auxiliary cover-ups (of what really hit the Pentagon and of where Flight 77 really went) when the disaster could be achieved by simply flying Flight 77 into the building, period. A good conspiracy theory has an obvious motive, but here there is no logical motive to concoct such a convoluted plan. The given conspiracy theory produces more explanatory problems than it resolves, and the only problem it allegedly resolves isn't even a real problem, as we've seen above.
In closing, it's worth noting that eyewitness accounts uniformly indicate that the Pentagon was struck by Flight 77. Here is a collection of Flight 77 eyewitness accounts.
 Mlakar, P.F., Dusenberry, D.O., Harris, J.R., Haynes, G., Phan, L.T., & Sozen, MA. (2003). The Pentagon Building Performance Report. American Society of Civil Engineers.
 Adams, Frank. (1945). B-25 Crashes in the Fog. New York Times, July 29, p 1.
 Swinhart, Earl. The North American B-25 Mitchell. Accessed May 20, 2006.
 Long, Adam. (1946). Pilot Lost in Fog. New York Times, May 21, p 1.
 Pentagon crash photos by Steve Riskus.
Promoters of the no-757 theory:
Critics of the no-757 theory: