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What I am trying to perform is a clip what captures the shoreline on a town in CT. I have the town boundary and I can use the buffer to extrude the polygon but I have wondering if there was an easier way.

This is the image of the town

This is the image of the town with the data I want to clip

as you can see its the negative space in the boundary of the town polygon that I am hoping the fill.

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One way to do this (with a basic license) is with the Union tool. Create a polygon that contains the entire shoreline and extent to which you need the sea to cover.

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Then use this new feature and your land feature as input to the tool. This should result in a new feature class that contains various features, of which one should be the sea boundary you need.
enter image description here

Delete all the other features you do not need. enter image description here

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