Yes @greg_n your understanding is correct. The sound traveling in the air can be interpreted like waves of pressure differential. If the bullet travels at higher speed than the sound speed these waves are superimposed creating the shock wave. The angle formed define the proportion of the bullet speed and sound speed, that travels perpendicular to the shock wave. The sine of the angle is equal to that proportion, the inverse of that is the mach number. Tracing back from the reciver the shock wave that arrived there must have come perpendicular to that wave therefore it came from point 1, the distance 12 is the distance travelled at sound speed. At the same time the bullet travells from point 1 to point 3 at the bullet speed forming the rigth triangle 123. The shock wave total time is the time for the bullet to arrive at point 1 plus the time for the sound from point 1 to point 2. The report time is the time for the sound to go from the muzzle to point 2.
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