# NavList:

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

**Re: Cosine formula to solve a right spherical triangle?**

**From:**David Iwancio

**Date:**2020 Jan 21, 10:27 -0800

The Law of Cosines and Napier's Analogies are the same thing. The analogies are what's left over after accounting for cos(X) = sin(90°-X) and for cos(90°) = 0

cos(C) = cos(A)*cos(B) + sin(A)*sin(B)*cos(γ)

cos(C) = cos(A)*cos(B) + sin(A)*sin(B)*cos(90°)

cos(C) = cos(A)*cos(B) + sin(A)*sin(B)*0

cos(C) = cos(A)*cos(B) + 0

cos(C) = cos(A)*cos(B)

sin(90°-C) = cos(A)*cos(B)