Most radars, even the old ones, give a reasonably good range value for initial gun laying, since noting and correcting for fall of shot is always going to be needed due to gun and projectile ideosyncracies even if perfect target data is available.
However, angular accuracy is difficult to achieve since the radar beam radiates in a cone from the antenna. The bigger the antenna (in multiples of the radio wavelength used), the narrower the beam, but especially with the long wavelengths used in many search radars, such an antenna would be too large to put on a ship. Thus, various "tricks" are used to narrow the region where the target must be in the beam or, in the case of 2-D search radars, one axis (bearing) is narrowed and the other axis (elevation) is ignored so that all targets at all elevations look like one big target if they are at the same slant range and close to each other in bearing.
The earliest trick, which is still used, is "conical scan" where the radar beam is swept about a cone ("nutated") centered on the center of the receiving antenna. As the beam sweeps over the target, it sends back a "beep" (short radio return) of higher power than when the beam is cocked off in the other side of the cone. Thus the signal from the target will "warble" in synch with the scan. By noting the range, a short-delay electronic circuit (or digital computer calculation today) computes the angular offset of the target from the center of the receiver and either manually or automatically the antenna can be centered on the target, at which point the target signal becomes steady, since it is always being lit up with the same power there. This allows a very narrow effective angle resolution at the cost of only intermittent signal return (for a small, weak target) and much more complexity in the radar. Many of the earliest fire-control radars had very clumsy methods of doing this, but by the end of WWII, the U.S. dish-shaped antennas on the Mark 37 directors, for example, for the 3" and 5" AA guns were pretty good. Note that this conical scan system is very easy to jam.
More modern systems use multiple, small, slightly-offset "staring" receivers in the antenna that are always on and each and every radar signal pulse can be compared from one receiver to the other in a complex manner to determine the angular position of the target from the antenna center--this is a "monopulse" tracker and is a much tougher nut to jam if designed correctly, but again at the cost of even more complexity in the radar.
Search radars designed to merely find out "Is anyone there?" want rather
broad beams to minimize the time it takes to find this important information
out, while fire-control radars need very precise target data from a needle-beam
(or a trick like conical scan to fake such a needle beam) that, like a
telescope, only can see a tiny portion of the sky at a time. Modern computer-controlled,
phased-array radars can do both, but again this increases immensely the
complexity of the radar, especially the software controlling the radar.