The maximum deflection angle of the bullet, theta, becomes:
Tan (theta) = ( 1 - beta 2 ) / (2 beta),
where beta is the outgoing speed of the bullet divided by the incoming speed of the bullet. Inverting the above equation gives
beta = [1 - Sin (theta) ] / Cos (theta).
Using these equations produce the following tabulated values.
| theta (degrees) | beta | theta (degrees) | beta |
| 1 | .98 | 3 | .95 |
| 5 | .92 | 10 | .84 |
| 15 | .77 | 20 | .70 |
| 25 | .64 | 30 | .58 |
| 40 | .47 | 50 | .36 |
These results show larger deflections significantly reduce speed of the bullet. A twenty-degree deflection results in a 30 percent loss of speed or momentum. In terms of kinetic energy, the cost of this twenty-degree deflection becomes 51 percent.
An obstacle deflects a bullet by providing an impulse, which changes the incoming momentum of the bullet. Replacement of this impulse by an equivalent deflecting momentum reduces the deflection problem to trigonometry.
In particular the base of an acute triangle, OB represents the incoming momentum of the bullet. A line segment, CB represents the deflecting momentum. The line segment, OC, corresponds to the outgoing momentum of the bullet.
Details of the collision between the bullet and the obstacle determine the angle of the deflecting momentum, OBC. This complication at first appears to render solution of this problem impractical. However the deflecting momentum must be equal or less than the incoming momentum of the bullet and vanish when angle OBC is ninety degrees. This suggests the deflecting momentum equals the impulse from the obstacle times the cosine of angle OBC.
Calculations show that as the angle of deflecting momentum increases from zero, the deflection angle of the bullet increases, reaches a maximum then decreases. This result is not surprising since the magnitude of the deflecting momentum decreases with its increasing angle. The idea of a maximum deflection angle of the bullet permits solution without knowledge of orientation of the bullet or shape of the obstacle.