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. For example, a side of a triangle subtends the opposite angle. More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc. For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints. If an angle is subtended by a straight or curved segment, the segment is said to subtend the angle. Sometimes the term "subtend" is applied in the opposite sense, and the angle is said to subtend the segment. Alternately, the angle can be said to intercept or enclose 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. More generally, a surface subtends a solid angle if its boundary defines the cone of the angle.