NavList:

During past several years I had few cases when I needed to perform opposite of sight reduction -- from observer's position, azimuth and distance to a point find the coordinates of this point. Every time it was a struggle -- I ended up using some random online calculator without actually understanding what is going on.

While there is significant newbie oriented body of texts, targeting the sight reduction methods and formulas, there seems to be a lack of simialr exposure for its opposite, the great circle sailings. Today I understood why -- I realized that this is exactly same triangle and exactly same formula.

Imagine that "you", the observer, is new north pole and north pole is the observer. This way, the original latitude remains "latitude" in a new frame of reference, azimuth toward a target point becomes "lha", and distance (co- distance, actually) to a point becomes its "declination". After you plug in these "latitude", "declination" and "LHA" into your favorite sight reduction method and crunch the numbers, you obtain "altitude" and "azimuth". Now, the co-"altitude" is the distance form the "observer" (AKA North pole) to the point, that is, its declination. And the "azimuth" is the angle between the meridians of the original observer and the point, that is LHA.

Things are a little bit more complicated by the conventions and signs of LHA vs t vs azimuth, but the general idea remains valid.

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