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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Spherical triangle split by right triangles
From: Ron Jones
Date: 2016 Jan 22, 19:47 -0800

NASR Triangles Formulas

Triangle I:
sin(A) = sin(LHA)·cos(L)
sin(B) = cos(L)·sin(Z1)
cos(LHA) = sin(Z1)·cos(A)
sin(L) = cos(A)·cos(B)
cos(Z1) = sin(LHA)·cos(B)
sin(A) = tan(90°-Z1)·tan(B)
sin(B) = tan(A)·tan(90°-LHA)
sin(LHA) = tan(B)·tan(L)
sin(Lat) = tan(90°-LHA)·tan(90°-Z1)
sin(Z1) = tan(L)·tan(A)

Triangle II:
sin(A) = cos(H)·sin(P)
cos(F) = cos(H)·sin(Z2)
cos(P) = sin(Z2)·cos(A)
sin(H) = cos(A)·sin(F)
cos(Z2) = sin(P)·sin(F)
sin(A) = tan(90°-Z2)·tan(90°-F)
cos(F) = tan(90°-P)·tan(A)
cos(P) = tan(90°-F)·tan(H)
cos(H) = tan(90°-Z2)·tan(90°-P)
cos(Z2) = tan(A)·tan(H) Browse Files

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