transfer attribute from line that splits polygon

[DanSeidensticker]

I have a polygon feature class (floodplains) and line feature class (cross sections).  When splitting the polygons based on the line features, I'd like to have an attribute (elevation) in the line feature be transferred to the new split polygon. The real trick is that I only want the elevation transferred to the polygon to the right (digitized direction) of the cross section line.

[WesMiller]

You could use Spatial Join—Help | ArcGIS for Desktop  to get the line data to the polygon data. To get data from just the right side you would have to do some programming