The second diagram below shows the minimum distance for an object to be seen by half the planet simultaneously.
Any farther, then, like the sun, half the planet would see the object and its distance could not be calculated using rise/set observations.
But the moon cannot be observed simultaneously over 180˚.
For example, when it is visible near the Arctic Circle (75˚ N. Lat), it is not seen in the Antartic (75˚ S. Lat) and vice versa.
This is similar to its observation from 51˚ N. Latitude. It can be above the horizon for as little as 8 hours for 2-3 days every orbit. At the same dates, it is visible for over 12 hours at 51˚ S. Latitude. This then reverses. When it is seen for 8 hours at 51˚ S. Latitude, it is visible for over 12 hours at 51˚ N. Latitude.
This variance is caused not only by its distance but also by the fact that its orbital path lies at an angle to earth’s equator. So each cycle it spends half the time below the equator and the other half above the equator.
Using the 8 hours as degrees (120˚) we use the rise/set times sightings as tangents that produce a distance about 1679.85 miles from earth.
See image below.
If you have any questions, please don’t hesitate to leave a comment!