fundamental astronomy - Calculating Angular Distance

You use Spherical Trigonometry

Given $A_1$ and $A_2$ are the respective azimuthal coordinates of the two objects, and $a_1$, $a_2$ their respective altitudes,

the angular seperation $theta$ is given by

$$cos theta = sin a_1 sin a_2 + cos a_1 cos a_2 cos (A_1-A_2)$$