spherical trigonometry

Spherical trigonometry is a branch of mathematics that deals with spherical triangles formed by the intersection of three great circle arcs on a sphere's surface. Unlike planar triangles, the sum of angles in a spherical triangle is always greater than 180 degrees. The excess over 180 degrees is called the spherical excess, and it's used to calculate the area of the spherical triangle: Area = E r², where E is the spherical excess and r is the sphere's radius.1

Historically, spherical trigonometry was crucial for navigation, cartography, and astronomy. Formulas analogous to those in plane trigonometry, such as the law of sines and the law of cosines, exist for spherical triangles. These principles allow for the calculation of unknown sides or angles when others are known.123