I may be totally off here and I will welcome any correction but:
The 40 deg arc is being shown on maps as the supposed northerly option of the flight path.
There is no way that the aircraft flew along the arc as if it was some huge DME arc. The flight path would have cut through various arcs, the 40 deg one being just one, with the hourly ping being on a different one each time.
I must be missing something here...anyone?
I agree with you goose, not only that, but we must assume that the arc, is really a sector of a sphere, as the Ping only tells them the distance from the satellite at a certain time, and this diagram is only 2 dimensional. And this particular arc or section of sphere is all the possible locations as of the LAST ping.
They would have the data of all the other hourly pings (7?) and by starting out with the last known actual position, where it was lost off the actual radar, assuming a reasonable airspeed, they could intersect the plane's assumed trajectory with the Ping arc and have an idea of possible locations.
The assumptions they are making are airspeed and direction - they can't tell that by the pings. . Lots of assumptions. Many possibilities.