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I'm assuming that you are using an Ethernet shield, as nothing about this is stated. But solution is really similar between many network solution.

Once a TCP connection has been established, it can be used like you would use the Serial;

you'll probably end up having something similar to:

EthernetClient client = server.available(); //accept a new connection
if (client) { //if valid connection
  client.print(distanceValue);
  client.close(); //close connection
}

look at the official API reference for a more detailed list of available command.