Q: AirPlay with 27" is not working with the set-top box

Do you have an AppleTV, if not you need to get one in order to make Airplay to work. If you have an ATV and it's still not working then please carefully read Apple's Use AirPlay to wirelessly stream content from your iPhone, iPad, or iPod touch - Apple Support

When you say "the set-top box," do you mean an Apple TV? What generation Apple TV? What generation 27" iMac? What version of OS X?

Assuming that the answers are "yes, 3rd, current, current":

What are you trying, how are you trying it, and what happens?