dspurg7310 wrote:

I am really new at electronics projects. I am trying to build a repeater
out of two mobile VHF radios and I'm not sure how to solve a problem I
am having:

My main problem is with the radio that I want to transmit. It does not
have VOX mode on it and I'm not sure how to get the first radio to
trigger the second radio to transmit. Is there a simple way to do this
or do I actually need a radio with VOX capability?

You need to build a circuit that connects the Squelch signal from your
receiving radio to the PTT input of the transmitting radio.
This could be as simple as a transistor and a resistor, it could add
some timer(s) and tone generator(s), or it could be a complicated circuit
with a microcontroller.
It all depends on how you want the repeater to behave.