It depends why the person is being vague, I think.
If they have an 8.00 appointment that is expected to last 30 minutes, and the journey to the meeting place is 30 minutes she might be hoping to be there for 9.00, but is allowing for the fact that the appointment might run late, so I would wait until she arrived. I would expect an update as soon as there was a reasonable ETA though.
If they are just asking for a bit of leeway because they can't be bothered to get ready on time, then I would allow 10 minutes or so before getting irritated. If I were waiting at home and we weren't going on somewhere time-specific I'd be less bothered than if we had, say, theatre tickets or a third party was expecting us and I was going to be late, too. If I were waiting outside I would probably head home (or on to where we were going) after ten minutes and text to say she should meet me there.
All the same, if traffic is involved it is not always possible to be precise, so again, much depends on the situation.