How to create polyline of varying distance from origin point using azimuth?

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I am looking for a Python script that does the following:

1. Uses a point (from a point shapefile) as the origin.
2. Creates about 3 km line from point
3. Based on an azimuth provided in the original point shapefile.
4. Creates new entry in another shapefile with the new line

I imagine this involves trig, but I can't decide the best way to go about it.



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