The systems the Royal Navy (and others) used during WWI required that the ships see each other at all times. A haze, smoke-bank etc intervening would mean that you could no longer shoot.
The systems developed interwar improved on this. You still had to see the target to set up the firing solution, once it was set ("target is moving in direction X degrees at Y knots") the system would automatically calculate present and future target position relative to the own ship based on the last input. This meant that you could keep firing even if you lost line of sight. ASSUMING, of course, that the target kept moving as it did and that your estimate of its movement vector was correct. Even so it was a great improvement.
I was always wondering how capital ships could score hits on one another without seeing each other without radar let alone satellites. Thanks
Prior to radar, the ships had to be able to see each other. In theory, they could have used aircraft but those arrived equipped for fire control basically when radar did.
The main director on an iowa-class battleship can see to 27,000 yds. to the horizon. That's about the distance when the ships opened fire at Denmark straight (where radar was used) At Jutland, the battle began at about 15,000 yds. At Guadalcanal, the range was about 18,000. At Surigao Strait the opening range was about 23,000.
Even with radar, engagement ranges were within visual detection.
Fire control computers started to appear in the early 20th century and increased in complexity throughout the battleship era.
The Dumaresq went to sea in 1905.
The Dreyer table in 1916.
The Rangekeeper in 1917.