Trigonometry is the branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides
Trigonometry is most simply associated with planar right-angle triangles . One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.
Trigonometry and trigonometric functions have several applications. For example, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.
vCalc's Trigonometry library contains equations that compute lengths and angles of triangles.