Using a Dipole Antenna on a 50 ohm FM transmitter
The output is very likely to be an unbalanced type suitable for quarter wave antennas with a matching section. It's got half the impedance of the dipole i.e. 38 ohms and a simple 12 ohm resistor in series will match it to the 50 ohm output.

You can match it to a half wave antenna but you need to use a balun to drive that type of antenna properly - this will also allow you to get the impedance correctly matched.