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I am not sure if your polylines already exist and you just want to rotate them or you have points as starting points to draw or create the lines.
If you are asking a drawing question (using points as reference?), you may want to post this at the Cartography forum:
If you need to create polylines with bearings, you can try Bearing Distance To Line (new in ArcGIS 10):
You need to prepare the required fields in a table as input.
Thanks I think "bearing distance to line" worked for me.
I entered the UTM coordinates, length and bearing, and it worked perfect for me. Now its possible to draw the lines according to the collar (strike) of the drill hole
You are welcome. I am glad the tool worked for you.