Subtended angle

In geometry, an angle subtended (from Latin for "stretched under") by a line segment at an arbitrary vertex is formed by the two rays between the vertex and each endpoint of the segment.

The above definition of a subtended plane angle remains valid in three-dimensional space (3D), as one vertex and two endpoints (assumed non-collinear) define an Euclidean plane in 3D.

For example, an arc of a great circle on a sphere subtends a central plane angle, formed by the two radii between the center of the sphere and each of the two arc endpoints.

By extension, an angle subtended by a more complex geometric figure may be defined in terms of the figure's convex hull and its diameter; for example, the angle subtended by a tree as viewed in a camera (see angular size).

[1] A subtended plane angle can also be defined for any two arbitrary isolated points and a vertex, as in two lines of sight from a particular viewer; for example, the angle subtended by two stars as seen from Earth (see angular separation).