Answer
Particle 1 has the largest Lorentz factor, followed by 2, then 3, then 4, then 5, then 6.
Work Step by Step
We are asked to rank the particles in order of Lorentz factor; greatest first. We can use the equation (37-56) on page 1141 of the book to isolate the Lorentz factor, $\gamma$.
$$\cos \theta = 1/\gamma$$
$$\gamma = 1/\cos \theta$$
We can see that as the angle, $\theta$, gets larger (from $0^{\circ}$ to $90^{\circ}$) the Lorentz factor also gets larger. So the triangles with the largest angle, $\theta$, will have the largest Lorentz factor.
Based on the triangles given, particle 1 has the largest angle and therefore largest Lorentz factor, followed by 2, then 3, then 4, then 5, then 6.
