# Computing coordinates of point knowing coordinates of observer point, azimuth and distance to unknown point?

I have the longitude and latitude of a known point O(x,y) where x and y are obtained from transforming the longitude and latitude from EPSG 4326 to EPSG 32635. This is the observer point. I have another point A(x1, y1) whose coordinates I don't know, but I know the distance from O to A in meters and the azimuth from O to A in radians.

How can I compute the coordinates of A knowing only these?

A function in Qgis in C++ would be the most useful, or at least a mathematical formula would be great.

• Can you treat the measurements to be on a plane or do you need geodesic calculations? Commented Nov 6, 2018 at 9:43
• I think with EPSG 32635 (UTM 35N) we are on a plane anyway. Commented Nov 6, 2018 at 9:45
• This plugin seems to do it, may be you have to chage your radians to degrees: northrivergeographic.com/qgis-azimuth-distance-plugin Commented Nov 6, 2018 at 9:54
• For reference: on a plane (projection) use Pythagoras, on a spheroid (e.g. WGS84) refer to the Direct Problem of Vincenty's formulae. Commented Nov 6, 2018 at 13:18

If QGIS Field calculator is an option;

INPUTS

• `x_32635`: your input x-coordinate on EPSG:32645
• `y_32635`: your input y-coordinate on EPSG:32645
• `d_m`: your input distance in meters
• `az_rad`: your input azimuth in radians (nb. clockwise from north)

Calculation

x_new (x-coordinate of new point on UTM35N)

``````x(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),
``````

y_new (y-coordinate of new point on UTM35N)

``````y(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),
``````

x_4326 (longitude of new point)

``````x(transform(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),
'EPSG:32635', 'EPSG:4326'))
``````

y_4326 (latitude of new point)

``````y(transform(translate(geom_from_wkt('POINT('||"x_32635"||' '||"y_32635"||')'),