# How to calculate point from lat/long, angle, and distance? [duplicate]

I am trying to calculate the point from a given lat/long, a bearing, and a distance.

This is for plotting weather given a aeronautical way point.

For example:

Given a waypoint with a known lat/long (LAX airport control tower), with a bearing of North by Northwest and a distance of 45 nautical miles, where is the point?

I could treat the world as flat, but I think the resulting calculations would be inaccurate the further north the point is since longitudes get more narrow near the poles.

I am mainly interested in plotting these points in the US. Is there a projection that would help me do this?

This is for a Python application I'm writing, and the libraries I have access to are GDAL and Proj4 for projections. So no fancy tools like ArcGIS are available to me.

Ultimately I want to combine 4 or these calculated points to form a polygon that should roughly be about 100-200 miles in width and height.

Thanks!

• Hi LeeMobile, what software are you trying to plot in? Jun 24, 2014 at 0:54
• This is for a Python application I'm writing. I have access to the GDAL and Proj4 libraries, but that's it. Jun 24, 2014 at 0:56
• That is interesting, there are mixed units involved, nautical miles can't be measured in DD and bearings don't hold true in UTM. What kind of accuracy are you expecting? I can suggest is project the point, draw a circle, project the circle back and intersect with a bearing line. Jun 24, 2014 at 1:02
• Would you be able to edit your Question to include those additional details that seem highly relevant to what you are asking, please?
– PolyGeo
Jun 24, 2014 at 1:06
• Off-topic, but I always thought that "north by northwest" was a great film, but isn't a real direction Jun 24, 2014 at 1:48