The transaction is committed on the sql server, how can the client then know if the transaction was committed or not?
It can't. The application gets a network error because the connection has dropped. From that, it has no way of knowing whether the requested operation was successful.
It might be possible for the application to reconnect and then query the "current state of play" of the Transaction to determine whether it was successful. Realistically, though, in a Local Area Network scenario, the chances of this happening are so vanishingly small that it's barely worth worrying about.
However, if you're writing an app that will run on a hand-held device, collecting data somewhere in the middle of the Amazon rainforest over a particularly flaky cell-phone connection, this is just the sort of thing that you might need to do, effectively building a "State Machine" for the progress of each Transaction and only accepting that everything has completed when it reaches the "end state".