I understand that ATC radar uses an encoding altimeter and a transponder
operating with Mode C to determine an aircraft's altitude. Let's forget
about Mode C for a moment and switch to Mode A only or just a primary
return.

If an aircraft is at 18,000 ft (approx 3 nm) and 3 nm away from the
radar antenna, as seen on a map, how does the radar correct for slant
distance when distance is displayed (e.g. using concentric circle
distance markers on the scope or relative to a known distance, such as a
marker on the display)?

In other words how does the radar know that the aircraft is actually 3
nm away laterally and not 4.25 nm (approx slant distance at that altitude)?