# NavList:

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

**Basic question regarding Napier's triangles**

**From:**UNK

**Date:**2009 May 28, 12:16 -0700

Hello my name is Christian Scheele and I live in Cape Town. I am by no means a professional navigator or mathematician and hope that I am not gatecrashing any party by making myself heard in here without much ado. I would much appreciate it if somebody could help me understand the application of Napier's triangles to specific scenarios. I have obviously run afoul of some very basic premise governing Napier's rules. Consider a spherical triangle superimposed on the following parts of an ideally spherical rather than spheroid globe, where capitals denote angles and small letters denote sides: A = 90 degrees, c = 70 degrees , a = 40 degrees. Applying Napier's rules, (90~A) is the "middle part" which is opposite b and c. Sin (90~A) = Cos b. Cos C removing complement: Cos a = Cos b. Cos c transposing formula: Cos b = Cos a/ Cos c substituting values: Cos b = Cos 40/ Cos 70 Cos b = 0.766.../ 0.342... Cos b = 2.24 ( 2 d.p.) But b is not defined for values > 1. It would appear that certain right-angles spherical triangles, namely such yielding Cos values > 1, cannot be solved as illustrated in the above problem and application. I have obviously made a blunder somewhere... Either way, could somebody please help me approach this problem? I would be most grateful. (This problem can be complicated should one assume that the triangle lies in the plane of a spheroid, such as the earth, rather than a sphere. For example, one could assume that b lies on 20 degrees N and a lies on 0 degrees longitude. This implies that c can be broken up into a component of 20 N and 50 S. In that case corrections must be made to any results arrived at by having assumed perfectly spherical properties initially. Perhaps Inman's Tables could come in handy here...) ----------------------------------------------- [Sent from archive by: scheele-AT-telkomsa.net] --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---