Which way to face if somewhat antipodean to Mecca?

The wikipedia article for the Qibla compass says that to calculate the direction to face for prayer (i.e. towards Mecca) one must use a "sphercial triangle" which I have never heard of. It is also uncited and I don't believe it. https://en.wikipedia.org/wiki/Qibla_compass I live in Western Europe and have always heard the adage "face East" but of course Mecca is also demonstrably south of Europe as well. My question comes from the somewhat surprising fact I learned recently which is that if you were to fly from New York to Mecca, you would begin by flying North East and over Greenland(!) following the curve of the Earth, turning back South East (although always following a straight line on the surface of the Earth) towards Mecca. Do New Yorkers face North East in muslim prayer? If not, which way do they face and why? Given our modern day understanding of the shape of the Earth, if Muslims do not face North East when praying in New York, should they? I want to say that I could see this question being taken as sarcastic but I genuinely would like to know the answer. I'm a Maths teacher and I think it would be something interesting to bring into a topic on 3D shapes or coordinates.