"Tienes que esperar media hora."
Translation:You have to wait half an hour.
How would i know whether to say "a esperar" or "que esperar" duolingo seems to be inconsistent with these.
Tener always uses que to mean to have to, not a. I don't think Duo is inconsistent with tener que + infinitive.
Here are a few verbs that need a before a following infinitive: ir a, venir a, ayudar a, invitar a, empezar a, comenzar a, enseñar a, aprender a, y otros.