New York, NY
According to which calculation of “facing East” do you suggest we follow? (See https://www.myzmanim.com/read/direction.aspx for a bigger discussion).
I follow the general approach that halakhic measurements go by how we as normal human beings would measure things, not by precise instruments and quantifying that did not exist in the time of Chazal. For example, rather than asking how many degrees is yad soledet bo, I would ask if you can keep you hands under the water for 30 seconds or so without having to pull them out. See Responsa Benei Banim 1:11,
ואטו צריך להסתפק באחת ממדות הטמפרטורות האלו הלא לא שיערו חז”ל בטמפרטורות, ואין לנו אלא מה שאמרו במסכת שבת דף מ’ עמוד ב’ אמר רחבא היכי דמי יד סולדת בו כל שכריסו של תינוק נכוית עכ”ל
So, basically I feel that Chazal never were that precise, and anything that a normal person would say is pointing in the direction of Jerusalem is enough. If we wanted to be more precise, I would say that we follow the direction on a compass, the rhumb line, since that is a measurement that is available to everyone nowadays, and easily accessible/determinable (and it was already in use in the time of the Rishonim).