As barba already said the long and short both are limited to a 27t big cog. The short cage can handle 29t of slack and long cage can handle 38t. To figure out how much slack the RD needs to handle add the number of teeth on your large ring to the number of teeth on your large cog, then subtract the number of teeth on your small ring and small cog. Example: 53/39 with a 12-27 cassette (53 + 27) - (39 + 12) = 27t. Note a 50/34 with a 12-27 actually creates 31t of slack, which technically requires a long cage but most people successfully use that combo with a short cage RD.

If you want to use a larger cog than a 27t you have to get a mountain bike derailluer which are designed to handle up to 34t cogs.