# Transform local polar coordinates to UTM

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.

• Since this is very local, why don't you use simple trigonometry on a plane? – AndreJ May 10 '16 at 18:30
• Because I don´t know how to. – Mauro Assis May 10 '16 at 18:43

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.

• Depending on the orientation of Azimuth, you might have to subtract the Delta value. – AndreJ May 11 '16 at 9:48
• Hasan, I have two Azimuths, which one should I use? – Mauro Assis May 11 '16 at 13:51
• First use the AB Azimuth (azimuth of B from A) to get the coordinates of B then use the BC Azimuth (azimuth of C from B) to get the coordinates of C – Hasan Mustafa May 11 '16 at 14:23

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.