Take a look, there are many attack profiles:
https://www.google.com/search?q=anti-ship+cruise+missile+attack+profile&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwiWxNXZkKPYAhVC42MKHSPZDpoQsAQIPg&biw=1438&bih=811
You are also assuming that the USS Princeton assumed perfect tactical awareness and perfect information on the target.
It is always best to get eyes on something rather than assume. It isn’t a video game.
Remember when the US Shot down that airliner in the Gulf?
Much more of a 'WTF?' GQ than a 'we're under attack' GQ.