Routing Roku audio to monitors connected to PC

I'm looking to set up my personal PC in my living room and use my TV (not Roku) as a monitor. However, I don't think my girlfriend is going to be okay with navigating streaming services on a PC.

So, I'd like to set up the Roku device to my TV that will be hooked up to my PC while using the studio monitors for sound. I'm not sure if there's a way that I can do this. Any information would be appreciated!