## Some Triangle Formulas

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There are quite a few formulas dealing with triangles. Here are some. R is the circumradius, r is the inradius, h is a height, p is the perimeter (a+b+c), s is the semi-perimeter (a+b+c)/2, and sqr() is the square root function.

Area=ah/2 [h=height perpendicular to a]
Area=sqr(s(s-a)(s-b)(s-c)) [Hero's Formula]
Area=sqr((a+b+c)(-a+b+c)(a-b+c)(a+b-c))/4
Area=sqr(p(p-2a)(p-2b)(p-2c))/4
Area=2R^2sinA sinB sinC
Area=abc/4R
Area=rs
Area=(bc sinA)/2
Area=(a^2 sinB sinC)/(2 sinA)
CotA=(a^2+b^2+c^2)/4area
c^2=a^2+b^2-2ab cosC [Law of Cosines]
a/sinA=b/sinB=c/sinC=2R [Law of Sines]
(a-b)/(a+b)=tan((A-B)/2)/tan((A+B)/2) [Law of Tangents]

There are also formulas for the Area, involving determinants, when the cooridinates of the vertices are given (in 2-space, and 3-space).