This is a relatively straightforward application of spherical trigonometry. (See also: About coordinate systems and angle differences and Angular Distance Between Two Points on a Sphere)
The expression to compute the angle on the celestial sphere between to points is:
$$\Psi = \arccos\left(\sin\theta_1\sin\theta_2 + \cos\theta_1\cos\theta_2\cos(\phi_1-\phi_2)\right)$$
where $\Psi$ is the angular separation, $\phi_1$ and $\phi_2$ are the right ascensions of the first and second direction, and $\theta_1$ and $\theta_2$ are the declinations of the first and second direction.
Star Pair |
Separation (deg) |
Alnitak - Saiph |
7.9203 |
Alnitak - Sirius |
21.6568 |
Saiph - Sirius |
15.6351 |
I am including my conversion of the RA and DEC to degrees in case I have made a mistake if anyone wants to check my computations.
Star |
RA (HH MM SS) |
RA (deg) |
DEC (DD MM SS) |
DEC (deg) |
Alnitak |
05 40 45.527 |
85.1897 |
-01 56 33.26 |
-1.9426 |
Saiph |
05 47 45.389 |
86.9391 |
-09 40 10.58 |
-9.6696 |
Sirius |
06 45 08.917 |
101.2872 |
-16 42 58.02 |
-16.7161 |