The Navigational Triangle
To describe the locations of celestial objects, astronomers imagined a celestial sphere, whose surface is of infinite distance from the Earth. Early navigators used the sphere to plot a navigational triangle, the points of which coincide with the celestial body, the elevated pole, and the zenith, a point directly above the observer. Using spherical trigonometry, the navigator solved the angle at the pole, and from that could calculate his longitude. By referring to charts that gave the star’s angular distance from the celestial equator, or declination, and determining the angle at the star, he could pinpoint his latitude.
Modern navigators have it easier. They find the altitude of a star and know they are somewhere on a circle, where from every point the star is the same angle above the horizontal.