Maybe I'm missing something. Taper is simply rise over run, so 1:50 means 1 unit vertical to 50 units horizontal. The angle is then arctan(1/50) = 1.14576 degrees. If the taper is INCLUSIVE, then divide by two to get the face angle.
For example, I have a premium thread of 3/4 TPF (taper per foot)imperial. This means 0.75 inch rise for every 12.0 inches of run ON DIAMETER. The required angle is then 0.5 arctan(0.75/12) = 1.78817 degrees. This would be the standard half angle cone for LTC threads for oilfield casing. API listing is 1 degree 47 min.
You don't need diameter, just the understanding if taper is measured inclusive thereof.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada