Astronomical triangle

The astronomical triangle, also called the PZX or navigational triangle, is the spherical triangle on the celestial sphere whose three vertices are the elevated pole P, the observer’s zenith Z, and the body X. Its three sides are the co-latitude (90 degrees minus latitude) at Z, the polar distance or co-declination (90 degrees minus declination) at P, and the zenith distance (90 degrees minus altitude) at X. The angle at P is the local hour angle, and the angle at Z is the azimuth. Solving this triangle by the cosine rule yields Hc and Zn, the heart of every sight reduction.