I don’t remember this particular aspect when I was reading about this, but I struggle to think of cases in which our crafts travel for any significant amount of time perpendicular to our line of sight to them. By definitition this cannot happen for too long, because either the craft flies straight and we revolve or the craft has arrived and it revolves too. In the frist case the angle will not stay at 90 for too long, in the second case we see it straight on at regular intervals.
For the brief periods the ship might be perpendicular we can use intertial navigation.
The other thing is that I suspect geometry can be used pretty close to 90 deg. Cos(80) is still significantly large at 0.2.