Although Dec. 21 would be a good sunset to watch, I don't think its critical to forming the 90 degree angle necessary for calculations. Mintaka should be due East regardless of date. It rises on the celestial equator.
here's a star diagram of Orion with Mintaka, our East pointer, shown. Also note the delta symbol (4) associated with Mintaka. I'm sure that's a mere coincidence
View attachment 1608045
From: excerpt from Land Navigation.com
East and West by Mintaka
Now, back to Orion's belt. The three-star belt's lead star is Mintaka (min-TA-ka).
In my estimation, Mintaka is the second-most useful star for direction finding, bested only by Polaris. The reason for its usefulness is that it ALWAYS rises due east and sets due west, no matter where you are on earth.
In the northern hemisphere, Orion rises in the east on his back, travels across the southern sky, then sets on his face in the west. In the southern hemisphere, he likewise rises in the east on his back, but he travels across the northern sky to then set on his face in the west.
The closer you are to the Equator, the higher is Orion's path across the sky. At the Equator, Orion passes straight overhead. But, regardless of where you are on earth, Mintaka always rises due east and sets due west.
Because the horizon is often obscured from view by trees, mountains, or other obstacles, on any given night, chances are you won't see Mintaka at the moment it rises due east from below the horizon, but are most likely to see it some time later, when it's higher in the sky.
For the first two or three hours after Mintaka has risen, you can retrace its path back toward the horizon and to the spot from which it rose. To do so, imagine a line from Mintaka back to the horizon at an angle of 90 degrees minus your latitude, north or south, it doesn't matter. Where that line intersects the horizon is due east.
Conversely, two or three hours before Mintaka sets, you can find west by projecting its path forward to the horizon, once again at an angle of 90 degrees minus your latitude. Where your imaginary line intersects with the horizon is due west.