Subtended angle

In geometry, an angle subtended by an arc, line or other curve is one whose two rays pass through the endpoints of the arc. The precise meaning varies with the context. For example, one may speak of the angle subtended by an arc of a circumference when the angle's vertex is a point on the circumference. A simple theorem of plane geometry states that arcs of equal lengths subtend equal angles in such a situation.

Similarly, a surface or solid object subtends a solid angle. A solid angle is the area on a unit sphere cut out by the envelope of the vectors defining the perimeter of the surface or object. The solid angle subtended by a circular cone of opening angle (aperture) θ is

$2 \pi \left (1 - \cos {\theta \over 2} \right).$

See also

• Central angle
• Inscribed angle

External links

• How an object subtends an angle, Math Open Reference, With interactive applet
• Angle definition pages, Math Open Reference, with interactive applets that are also useful in a classroom setting.