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### Calculating the True Bearing Between Two Points

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Date: 9/20/95 at 8:43:4
From: Anonymous
Subject: Calculation of true bearing

How can I calculate the true bearing between two points on the
earth's surface?  I know their grid coordinates, and their lat-
long coordinates, and how to get from the grid coordinates to a
grid bearing, but how can I calculate the true bearing between the
two points?

David
```

```
Date: 11/19/95 at 16:13:59
From: Doctor Jonathan
Subject: Re: Calculation of true bearing

To find the true bearing from point A to point B on a sphere,
project the chord AB on to the tangent plane of A. Call this
projection AB'. The angle between AB' and the line segment
pointing north in the tangent plane will be the true heading. The
latter segment may be found by projecting the chord between A and
the north pole onto the tangent plane of A. In fact, with this
method you may find the heading relative to any point, not just
the "north" pole. This would be useful for finding the heading
according to a real life compass which gives headings relative to
magnetic north, not true north. For example, if you know the
coordinates for magnetic north (which I don't, offhand) N, you
could would find the angle between the projection of AN and AB in
the tangent plane of A--this would be the heading as measured by a
"real" compass.

-Doctor Jonathan,  The Geometry Forum

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Associated Topics:
College Higher-Dimensional Geometry

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