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» Online Classroom   »   » Public Discussion of Inland and Coastal Navigation   » 5-7

   
Author Topic: 5-7
M. C. Rowley


 - posted August 14, 2005 06:18 PM      Profile for M. C. Rowley           Edit/Delete Post 
Since we know two sides of the triangle and the angle between them why not simply use the Law of Cosines to calculate the third side (our distance error) instead of plotting? A 12 degree error at 45 miles would place us off course 9.4 miles.

Mark Rowley
Santa Fe, New Mexico

David Burch


 - posted August 16, 2005 02:03 PM      Profile for David Burch           Edit/Delete Post 
the goal here is not necessarily use a formula that requires computation, but something that you can work in your head for a quick answer. And that is where the 6° rule comes into play. It states simply that a 6° right triangle has sides in proportion of 1 to 10. (ie a way to memorize the tangent of 6°). This then can be scaled down forever and up to about 18°, where the ratio is not 1 to 10 but 3 to 10. A 3° angle has sides in proportion of 0.5 to 10, and so on.

Twelve degrees is 2 to 10, or 0.2 x 45 miles = 9.0 as a perfectly good approximation to the rigorously correct answer as we will never know the precise values that go into such a long run.

From: Starpath, Seattle, WA


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