I have two GPS positions and i want to calculate the angle between the one GPS point and a third point that i'm estimating it location with reference to the second GPS point. The Figure below explains the problem which is calculating angle(Alpha) in the figure. Here is what i know. first I calculated the heading of point A Heading (A) -- initial angle bearing, using old and new GPS coordinate of point A-- then I found the bearing angle from point A to B BeraingAngle(AB,AF).Now since both handing and bearing angle are relive to the north then Angle(Beta)=angle(AB,BF)= abs(Heading(A)-BearingAngle(AB,AF)). Also using haversine method i computed the distance two GPS point A and B dist(A,B). now I know the distance between point B and Cdist(B,C) and the angle(Theta)angle(BC,BE). So is it possible to calculate angle(Alpha) angle(AC,AD).


  • Heading (A) =270 degrees, Bearing (A,B) =300 degrees, Hence Angle (Beta)=300-270=30 degrees
  • dist (A,B)= 15 meters
  • dist(B,C)=5 meters
  • angle(Theta)=7 degrees

Note that BE is parallel to FD and BF is parallel to ED

enter image description here

  • $\begingroup$ i really dont understand what we know from the figure $\endgroup$ – dato datuashvili Sep 20 '17 at 15:01
  • $\begingroup$ It would be very nice if you can just sum up all the known and unknowns in an ordered way. $\endgroup$ – samjoe Sep 20 '17 at 15:05
  • $\begingroup$ You say you have a figure but you didn't add it? $\endgroup$ – Joffan Sep 20 '17 at 15:06
  • $\begingroup$ I have updated the figure, Thanks a lot $\endgroup$ – H.A Sep 20 '17 at 15:16
  • $\begingroup$ It would be helpful if you proofread the OP and make edits. $\endgroup$ – Χpẘ Sep 20 '17 at 15:16

Proof by pictures: enter image description here Renaming some variables enter image description here taking components of a enter image description here taking components of b enter image description here as opposite sides in rectangle are equal enter image description here *There is a typo in the picture above, in the right upper corner it is $b \cos(c)$ and not $b\cos(d)$

rewriting enter image description here Can you handle now?

  • $\begingroup$ Thank you, I was almost there figuring it out .Yes , It is Arctan (CD/AD) $\endgroup$ – H.A Sep 20 '17 at 16:12

You don't have enough information. The line $DEC$ could slide to the right with $C$ rising to keep $\theta$ constant. There is nothing that constrains it. Similarly $BF$ can slide either direction without causing a problem.

  • $\begingroup$ I have updated the figure to show what is know and what is not. Would you please explain in more details. $\endgroup$ – H.A Sep 20 '17 at 15:32
  • $\begingroup$ i know the length of AB and BC. if i can find the length of AD and DC i can find angle(alpha) right? $\endgroup$ – H.A Sep 20 '17 at 15:47

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