Calculate included angle from viewpoint to area

[JoeNunn]

If you have point data and polygon data, is there a simple means to calculate the angle (angle A in the picture below)  that includes the whole polygon from a point without having to draw lines from the point to the polygon and use these?  It looks so simple but I haven't managed to get a simple solution yet.....

Many thanks!

[ChrisDonohue__GISP]

If the data is all in 2D, one way to go would be to employ Generate Near Table using the starting point and points representing the extents of the polygon.  Be sure to read the fine points of the Tool Help on how the Angle is determined.  Also, check on how to set the Angle and Closest options are set so when running the tool one gets the angle to all the points.

One way to get points of the polygon is to convert the polygon to lines first using Feature to Line, then convert the lines to points using Feature Vertices to Points with the All option.  Then thin down the points to just the relevant two to use in Generate Near Table

Generate Near Table—Help | ArcGIS Desktop 

Feature To Line—Data Management toolbox | ArcGIS Desktop 

Feature Vertices To Points—Help | ArcGIS for Desktop 

Chris Donohue, GISP