The two main branches of trigonometry are plane trigonometry and spherical geometry. Trigonometry in general deals with the study of the relationships involving the lengths of angles and triangles.
Plane trigonometry focuses on the relationships between the angles and sides of triangles that have three vertices located on the surface of a plane. Students studying plane trigonometry learn about concepts like right angles, straight angles, acute angles, complimentary angles and supplementary angles. Since the triangles are all located on a plane, the sum of the angles is always 180 degrees.
In spherical trigonometry, students study curved triangles drawn on the surface of a sphere. This design means the sum of the angles of these triangles is higher than 180 degrees. Spherical trigonometry is used in astronomy and navigation.