Subtended arc

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

Similarly, a solid angle subtends a surface or a solid object. 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 delimited by a circular cone of opening angle (i.e. apex angle) θ is

: $2\; pi\; left\; (1\; -\; cos\; \{\; heta\; over\; 2\}\; ight).$

See also

*Central angle

External links

* [http://www.mathopenref.com/subtend.html How an object subtends an angle] , "Math Open Reference", With interactive applet
* [http://www.mathopenref.com/tocs/anglestoc.html Angle definition pages] , "Math Open Reference", with interactive applets that are also useful in a classroom setting.