Triangle angle calculation knowing only one angle

Question

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).

Example

• 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

Answer 1

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

rewriting Can you handle now?

Answer 2

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.