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July 2nd, 2017, 01:13 PM   #1
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Spherical triangle

I want to find angles of spherical traingle. The geographical coordinated of the points are
0, 0
0.000001, 0
0, 0.000001

I expect that agnles will be 90, a bit more than 45 and a bit more than 45 degrees.

I use great circule distance formula and spherical cosine formula
https://en.wikipedia.org/wiki/Great-circle_distance
https://en.wikipedia.org/wiki/Spherical_law_of_cosines

The central angles are pretty small and they seems correct. They are
2,46827E-8
1,74533E-8
1,74533E-8

But spherical law of cosines give strange results. I got the following angles in radians
0,687
0,687
1,9438
or in degrees
39,3627
39,3627
111,3746

It seems there is a mistake. Could you please help me.
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July 2nd, 2017, 03:02 PM   #2
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It would be helpful if you showed intermediate results.
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July 3rd, 2017, 06:03 PM   #3
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You need to specify the radius of the sphere.

Quote:
The central angles are pretty small and they seems correct. They are
2,46827E-8
1,74533E-8
1,74533E-8
What are these quantities ? Central angles?
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July 4th, 2017, 01:06 PM   #4
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Yes. They are central agnles in radians
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July 4th, 2017, 01:40 PM   #5
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Quote:
Originally Posted by zock View Post
Yes. They are central agnles in radians
Central angles of what? Try to be specific.

Also you need a radius for the sphere (1?).

Last edited by mathman; July 4th, 2017 at 01:49 PM.
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July 5th, 2017, 06:21 PM   #6
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I will assume the central angle is with reference to center of the sphere with radius 1. In that case the two equal sides have angles exactly equal to the sides (0.000001). The third side is very slightly less than sqrt(2) times other side length.
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