# 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 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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