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Trouble solving for spherical triangle
From: Hahns Burg
Date: 2020 Jul 11, 16:36 -0700

I’m interested in spherical trigonometry and have written a very basic BASIC program (see Excel file attached) which calculates destination (lat and lon) for a given DR (lat, lon), course, and distance.  I’ve solved for the spherical triangle (example: Law of Sines and Law of Cosines hold for my solution).

The Rub

Here’s the rub:  while the math itself holds, where course is set to exactly east or west (i..e., 90 or 270), I’m noticing destination latitude does not equal original DR latitude (where we know latitude should not be changing).  The errors increase with distance greater than 100 nmi.

I have a simple Excel spreadsheet modeling the following:

Three Points:

A = North Pole

B = DR

C = Destination

Three sides and angles from center of earth

a = distance sailed

c = [90 - DR latitude] and distance from North Pole

b = [90- destination latitude] and distance from North Pole

My math starts with B.   Then solves for c, then a; and lastly solves for the balance of A and C.    See attached Excel file.

What am I doing wrong?

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