Oh dear! High school trigonometry at my advanced age! I only hope that I have understood the question correctly. If so, the short answer is yes.
The simplest approach is to take each of points A, B and C separately as the solution for A does not require information about B or C. As I understand the question, you know the positions of X and Y - and therefore you know the distance between them - call it P - and the bearing of Y from X - call it L. You also know the bearing of unknown point A from point X - call it J - and the bearing of unknown point A from point Y - call it K. Consider the triangle XYA. You know that the distance XY = P. You know the angle at X (the difference between the bearings from X of points A and Y) = J+L. Based on the simple properties of parallel lines it should be clear that the angle at A (the difference between the bearings of A from X and from Y) = K-J. As a triangle's internal angles sum to 360 degrees, you know that the angle at Y is 360-(J+L)-(K-J) = 360-K-L. Therefore in triangle XYA you know one side and two angles - so this triangle is completely defined and can be solved. Solve it for the distance XA - the distance from X to A. Call this distance Q. Then, applying the sine rule: P / sin (K-J) = Q / sin (360-K-L) So Q = P * sin (360-K-L) / sin (K-J) Now that you know Q, it is simple to calculate the distance of A north/south from X ( = Q cos J) and the distance of A east/west from X ( = Q sin J). Thus you have the northing and easting for point A. Repeat for points B and C. I hope that I have (a) got it right and (b) made it clear - it is over 50 years since I did this stuff in what would probably nowadays be called high school. What a way to spend a Bank Holiday afternoon! Cheers! Mike Harris -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of [email protected] Sent: 25 May 2009 12:00 To: [email protected] Subject: newbies Digest, Vol 27, Issue 27 Send newbies mailing list submissions to [email protected] To subscribe or unsubscribe via the World Wide Web, visit http://lists.openstreetmap.org/listinfo/newbies or, via email, send a message with subject or body 'help' to [email protected] You can reach the person managing the list at [email protected] When replying, please edit your Subject line so it is more specific than "Re: Contents of newbies digest..." _______________________________________________ newbies mailing list [email protected] http://lists.openstreetmap.org/listinfo/newbies
