AASTriangle

AASTriangle[α,β,a]

returns a filled triangle with angles α and β and side length a, where a is adjacent to one angle only.

Details

  • AASTriangle is also known as angle-angle-side triangle.
  • AASTriangle can be used as a primitive in 2D graphics and as a geometric region in 2D.
  • The given (blue) and computed (red) parameters for an AASTriangle:
  • AASTriangle returns a Triangle with at the origin, on the positive axis, and in the half-plane .
  • AASTriangle allows the length a to be any positive number and the angles α and β to be positive such that α+β<π.

Background & Context

  • AASTriangle constructs an angle-angle-side triangle. In particular, AASTriangle[α,β,a] returns the Triangle in TemplateBox[{}, Reals]^2 with vertices , and located at the origin, on the positive axis and in the upper half-plane, respectively, with αBAC, βABC and a the length of the side opposite . By the AAS theorem, the triangle so specified is unique (up to geometric congruence). AASTriangle allows the length a to be any positive number and the angles α and β to be positive numbers satisfying α+β<π. The arguments of AASTriangle may be exact or approximate numeric expressions.
  • The Triangle objects returned by AASTriangle can be used as 2D graphics primitives or geometric regions.
  • AASTriangle is related to a number of other symbols. ASATriangle, SASTriangle and SSSTriangle return two-dimensional triangles constructed using different angle and/or side specifications. Finally, AASTriangle is a special case of Triangle, in the sense that AASTriangle[α,β,a] is equivalent to Triangle[{{0,0},{a Csc[α] Sin[α+β],0},{a Cot[α] Sin[β],a Sin[β]}}].

Examples

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Basic Examples  (4)

A triangle with , , and :

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An AASTriangle:

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Different styles applied to AASTriangle:

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Area and centroid:

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Centroid:

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Scope  (14)

Applications  (2)

Properties & Relations  (2)

Neat Examples  (1)

See Also

Triangle  SSSTriangle  SASTriangle  ASATriangle  Polygon

Introduced in 2014
(10.0)