I would like to calculate shortest distance from Polygon to polyline. ArcMap version is 10.2.2 Basic I don't have access to proximity tool. Can anyone offer me any suggestion's?
Since you have a desktop license, you are entitle to an ArcGIS.com Organization account. You can publish the polygon feature class/shapefile as a hosted feature service to ArcGIS Online. You can then perform a Find Nearest analysis.
The alternative is to do a simple spatial join with the CLOSEST match optoin. This will create a new featureclass with the distance between the polygon and polyline.
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