# SASTriangle

SASTriangle[a,γ,b]

returns a filled triangle with sides of length a and b and angle γ between them.

# Details

• SASTriangle is also known as side-angle-side triangle.
• SASTriangle 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 SASTriangle:
• SASTriangle returns a Triangle with A at the origin, B on the positive axis, and C in the half-plane .
• SASTriangle allows the lengths a and b to be any positive numbers and the angle γ strictly between 0 and .

# Background & Context

• SASTriangle constructs a side-angle-side triangle. In particular, SASTriangle[a,γ,b] represents the Triangle in with vertices , and located at the origin, on the positive axi, and in the upper half-plane, respectively, with a and b the lengths of the sides opposite vertices and and γ. By the SAS theorem, the triangle so specified is unique (up to geometric congruence). SASTriangle allows the lengths a and b to be any positive numbers and the angle γ to be a positive value satisfying . The arguments of SASTriangle may be exact or approximate numeric expressions.
• The Triangle objects returned by SASTriangle can be used as 2D graphics primitives or geometric regions.
• SASTriangle is related to a number of other symbols. AASTriangle, ASATriangle and SSSTriangle return two-dimensional triangles constructed using different angle and/or side specifications. SASTriangle is a special case of Triangle, in the sense that SASTriangle[a,γ,b] is equivalent to Triangle[{{0,0},{x,0},{y,z}}] for xSqrt[a^2+b^2-2 a b Cos[γ]], y(b^2-a bCos[γ])/Sqrt[a^2+b^2-2 a b Cos[γ]] and z(a b Sin[γ])/Sqrt[a^2+b^2-2 a b Cos[γ]].

# Examples

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## Basic Examples(4)

A triangle with , , and :

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An SASTriangle:

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Different styles applied to an SASTriangle:

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Area and centroid:

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