# Trigonometry/Spherical

Spherical trigonometry relates to spherical triangles, and trihedral angles. A spherical triangle is a triangle projected on a sphere. Spherical trigonometry has applications in navigation, and astronomy.

## Definitions and explanations[edit | edit source]

A **lune** is a shape on a sphere from one angle merged to an angle on the opposite side of the sphere. It is formed by two circles on a sphere. The area between two lines of longitude on one side of a globe are an example of a lune. A **digon** or a **bi-angle** are other terms for a lune.

A lune is composed of two spherical triangles, when split in half equidistant from each angle. These two congruent spherical triangles are called **colunar triangles**.

Unlike plane trigonometry, in spherical trigonometry it is possible for a spherical triangle to have up to three obtuse or right angles.

A **birectangular triangle** has two right angles.

A **trirectangular triangle** has three right angles.

**Polar triangle** are triangles with angles at the center of the sphere, and they are in relation to spherical triangles.

## References[edit | edit source]

- Moritz, Robert (1913),
*A Text-book on Spherical Trigonometry*(First ed.), New York: John Wiley and Sons *Wikipedia: Spherical Trigonometry*