Transform local polar coordinates to UTM

Question

I have some field points disposed like the diagram below:

In this diagram, I know:

1) Point A UTM coordinates

2) Distance between A and B

3) Distance between B and C

4) AB azimuth

5) BC azimuth

I´d like to know how to calculate point C UTM coordinates, considering that points B and C can be located in any position in the cartesian plane.

The distances are below 100 meters.

Answer 1

To get the coordinates of the points you can use these equations:

Delta Y = Distance * Cos (Azimuth)
Delta X = Distance * Sin (Azimuth)
New Y = Y + Delta Y
New X = X + Delta X

First you'll have to get the coordinates of B using these equations then go from there to C.

Answer 2

This kind of calculation is often referred to as CoGo (for coordinate geometry).

If you have several of them to do, and you don't wish to do any programming (or a lot of hand calculations) you can use Copan for Windows -- a free tool for CoGo and many other kinds of land survey calculations.

You can enter known coordinates in one place and known bearings (azimuths) and distances to get new point coordinates.

Disclosure: I built much of Copan.