# NavList:

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

**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(Z_{1})

cos(LHA) = sin(Z_{1})·cos(A)

sin(L) = cos(A)·cos(B)

cos(Z_{1}) = sin(LHA)·cos(B)

sin(A) = tan(90°-Z_{1})·tan(B)

sin(B) = tan(A)·tan(90°-LHA)

sin(LHA) = tan(B)·tan(L)

sin(Lat) = tan(90°-LHA)·tan(90°-Z_{1})

sin(Z_{1}) = tan(L)·tan(A)

Triangle II:

sin(A) = cos(H)·sin(P)

cos(F) = cos(H)·sin(Z_{2})

cos(P) = sin(Z_{2})·cos(A)

sin(H) = cos(A)·sin(F)

cos(Z_{2}) = sin(P)·sin(F)

sin(A) = tan(90°-Z_{2})·tan(90°-F)

cos(F) = tan(90°-P)·tan(A)

cos(P) = tan(90°-F)·tan(H)

cos(H) = tan(90°-Z_{2})·tan(90°-P)

cos(Z_{2}) = tan(A)·tan(H)