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 Trigonometry Trigonometry Math Forum

 January 4th, 2018, 01:21 PM #1 Newbie   Joined: Jan 2018 From: Milan Posts: 1 Thanks: 0 Spherical Triangles Hello Everybody! I'm not a student, I'm just trying to figure out how to calculate coordinates on a globe, and I would like to ask for some help. Let's say I have POINT A on the globe with the following coordinates: POINT A Latitude 45° 27' 50.95" N Longitude 9° 11' 23.98" E Also I have POINT B which is the Antipode: POINT B Latitude 45° 27' 50.95" S Longitude 170° 48' 36.02" W Given we are on a sphere (globe), from Point A to Point B for example I can draw 360 great circles, one for each single degree of the sphere: - and the distance to go from Point A to Point B is 180° (first semi-circle) - and the distance to go back from Point B to Point A is also 180° (second semi-circle) Now let's say I have POINT C with the following coordinates: POINT C Latitude 45° 26' 48.53" N Longitude 9° 1' 58.11" E Given these information, THERE IS ONLY ONE GREAT CIRCLE which: START IN POINT A GOES THROUGH POINT C ARRIVE IN POINT B (completing the first semi-circle of 180°) COME BACK IN POINT A (completing the second semi-circle of 180°) My problem is to find the formula to calculate the coordinates of the 2 Points which are half-way (90°) from Point A to Point B. Let's call these 2 Points as M and N: START in POINT A GOES THROUGH POINT C PASS THROUGH POINT M (at 90°) ARRIVE IN POINT B (completing the first semi-circle of 180°) PASS TO POINT N (at 270°) COME BACK IN POINT A (completing the second semi-circle of 180°) Which is the formula to calculate M and N? On a - plain surface - i would have used the simple proportion of triangles to calculate them, but given is a sphere I don't know the formula to be applied. I did some online search but I find a kind of difficult to figure it out. I have been out of school from 15 years now , so I would like to ask if somebody can help me. I hope my explanation is clear, thx a lot if you can help!!! Cheers February 20th, 2018, 10:08 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,933 Thanks: 2207 Sorry about delay. Tags spherical, triangles Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post proglote Physics 9 December 10th, 2018 06:20 AM zollen Calculus 2 October 15th, 2017 12:44 PM maluita659 Calculus 2 March 7th, 2014 11:51 AM westborn7 Trigonometry 0 August 4th, 2013 06:14 AM MetryRoad Algebra 3 April 17th, 2010 02:20 AM

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