# How to convert double bearing into x and y coordinate

If I have a double bearing from different point which is point A and point B on a single point (object), how do I get the x and y value?

Lets say the number of point A is 84 degrees and for point B is 245 degrees.

• Cartesian math is simple in projected space, but inappropriate to angular coordinates (longitude and latitude). Please edit your question to specify the nature of the coordinates, and to contain enough information to solve the problem. – Vince Mar 30 '16 at 15:38
• chuck, are you actually looking for an unknown point's coordinates when you are given two points, plus the bearings from the 2 known points to the unknown point? You want to do a triangulation. – mkennedy Mar 30 '16 at 16:49
• In CoGo terms, this calculation is sometimes referred to as the line-line intersection or bearing-bearing intersection problem. Are you asking for the mathematics or for software tools? – Martin F Mar 30 '16 at 17:44

1) If the projection is cartesian, the solution is a basic problem of Euclidean geometry and triangles:

If the angle of bearing is β, the solution is

``````x = distance * cos(β)
y = distance * sin(β)
``````

As you don't know the distance (d), but only the angle of bearing, you can only compute the Unit vector : x = 1 * cos(β) and y = 1 * sin(β)

2) if the projection is not cartesian, you need another solution ( Spherical coordinate system, see Calculate Latitude and Longitude from Range, Azimuth, and Elevation) with the same problem, you have only an angle of bearing (you can only use an unit sphere).

3) In short, with only the bearing value, you cannot.

• OP says he has points A and B, it means he knows their coordinates. Your answer ignores it. – FelixIP Mar 31 '16 at 1:09

Assuming you are working in projected coordinate system:

Pictures from , sorry cannot find one in English.

In pre-GPS era it was commonly used to calculate coordinates for hard to access points. Actually it was my 1st coding attempt designed to facilitate measurements of surface velocity of the glacier.