why do radio stations on the west coast have call letters that start with and the east coast is w?

Answer 1

When they gave out call numbers to the radio stations, they ran out of possibilties starting with W, so they gave the new ones, in west, K numbers.

Answer 2

TV and radio stations east of the Mississippi River have call signs starting with W and west of the Mississippi River they start with a K, so that the other 3 letters in the call signs can be re-used, and to tell the point of origin of the signal.