Find Angle Between a Line and a Plane

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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To measure the angle between a line and a plane, we have to measure in a plane perpendicular to the given plane, or in other words, in a plane containing the line and the pole. It's easy to see that the angle between the plane and the line is equal to 90 degrees minus the angle between the poles and the line.

Note than the angle can also be 90+A. Either answer is correct. The most suitable choice will depend on the application. 


Find the angle between a line trending 028 and plunging 40 degrees, and a plane striking 034 and dipping 50 NW.

1. Plot the pole to the plane (the stereonet is rotated so strike 034 is vertical. The pole and the plane are in blue).

2. Plot the line (the stereonet is rotated so trend 038 is horizontal. The line is in red).

3. Rotate the overlay so the pole and the line lie on a common great circle (purple). Count off the angle between the poles and the line (56 degrees). The angle between the line and the plane is 90 minus this angle, or 34 degrees. 90+56, or 146 degrees, is also correct.

4. Return the overlay to its original position.

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Created 8 September 2000, Last Update 8 September 2000
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