So this came up the other day - Dengar had a turret shot on Kanan, who was in arc, but not in arc at R3, so Dengar had to use his turret to shoot at him. However, Dengar's ability specifies "in arc" it does not give a range, so could he have taken the revenge shot?

Yes. The firing arc extends across the play area, so if the ship is inside, than Dengar gets his revenge shot, even if the attack is outside of arc.

So this came up the other day - Dengar had a turret shot on Kanan, who was in arc, but not in arc at R3, so Dengar had to use his turret to shoot at him. However, Dengar's ability specifies "in arc" it does not give a range, so could he have taken the revenge shot?

Yes.

"A firing arc extends across the play area."

- "Firing Arc", rules p. 11

If you refer to the FAQ, there's a new(ish) example wherein a ship is partially in arc at R2 but it's closest point to the attacker (a K wing) is at R1, so the attack is considered R1 for extra dice but R2 in arc for tactician. It seems odd at first but checking for arc and measuring range are independent of each other.