The [Commander-in-chief powers][1] are quite broad. The [War Powers Resolution][2] limits his ability to engage unilaterally in military action, by requiring him to report to Congress within 48 hours, and if Congress disapproves, troops must be removed after 60 days. However, this law pertains to armed forces, and would not apply to remotely-launched missiles. Additionally, it is unknown if the resolution is unconstitutional (presidents say it is). No law at all requires POTUS to obtain permission from someone else, in order to engage in a military action.



  [1]: https://www.law.cornell.edu/wex/commander_in_chief_powers
  [2]: https://www.law.cornell.edu/uscode/text/50/chapter-33