create line at a vertical angle from a horizontal line

[Kat]

Hi!

I'm trying to determine an erosion fall zone from a cliff. The standard is to draw a line from the top of the cliff down and see where it intersect the ground below and that determines the boundaries of the 'fall zone'. I can't figure out how to create a line at 37 degree from a horizontal line from the top of the cliff. Ideas? thanks.

[MichaelStead]

It sounds like what you really want is the point on the valley floor, not the sloping line, but either way.....
Just create a z aware line with a 3d start point (x,y,z) at the top of you cliff, use some trigonometry to figure out a coordinate that is at 37 degrees well below the surface of the valley floor, and edit the end vertice to be at this coordinate, then either manually record the coordinate where the line intersects the ground surface or use some 3d intersection tool.

If this point will do thats great. I would imagine that you want a line along the valley floor which you could rough out repeating this many times, but you should be able to create a 3D polygon slope that you can intersect with your terrain DEM and come up with a nice line. Make a z-aware line for the crest of the cliff, then copy this line parrallel to itself and modify the z values by a factor that gives the 37 degree slope. Make sure to displace the line horizontally enoungh to ensure the slope will intersect the ground.

[Kat]

Thanks Michael, any ideas on how to figure out the other coordinate of the line? I guess my trigonometry needs more then just one known angle to a triangle.
Thanks.

[JakubSisak]

Thanks Michael, any ideas on how to figure out the other coordinate of the line? I guess my trigonometry needs more then just one known angle to a triangle.
Thanks.

Is your horizontal line parallel with either northing or easting or does it have an azimuth? It's possible to do something like this if your horizontal line is oriented either north - south or east - west.  You can convert all data into points then re-map the XYZ coordinates to "trick" ArcMap into sectional view. (redigitize the cliff profile) Once you are looking at a sectional view you could start drawing a line at a particular angle. Creating scaled sections is not the easiest task in ArcGIS and things become a lot more complex when the data is oriented on an azimuth other than 0,90,180,360.  There are trigonometry formulas to convert data such as azimuth dip and distance into XYZ and it must work the other way arouund.  Here is some info on the trigonometry calculation (see whubber's answer).   The bottom line is; ArcGIS is not a 3D drawing program.  You could try Sketchup. You can export TIN into mulptipatch then collada then import into Sketchup. (Assuming your cliff is a TIN or a raster)  In Sketchup you can easily draw lines in true 3D by using the protractor for example.

[MichaelStead]

What you know for you trig equation is your 37 degree angle and the distance between the highest point on the cliff and the lowest elevation on the valley floor below. For the sake of an example lets say the cliff is 144 meters maximum above the valley floor. With a triangle labelled with sides ABC and angles abc (A is the vertical cliff face, B is the plane locally parallel to the earth) we know that angle b is 37 degrees and we will make side A 200 meters. We can then calculate side B by multiplying tan(37) * 200. So then you would pick your point along the line that represents your cliff crest and snap the start point of a new z aware line to it, then use the perpendicular tool to get that right angle off the cliff, hit ctrl g and enter the distance you calculated above.Then click on the top vertice and enter the correct elevation, then click on the end vertice and enter this value less 200.

You could now take this line and your TIN or DEM or whatever and find the intersection in ArcScene manually, or use one of the new 3D tools (http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/Intersect_3D_Line_With_Multipatch/00q9...). I think you might have to convert your terrain to a multipatch, but I am not sure as I haven't played with these much yet.

I have also done something similar to what is described by jakubsisak where you trick ArcMap by flipping the planes and making your z coordinate into your x or y coordinate and then using some of the more common (and proven) spatial tools.