What would the FBI do if...?

I was thinking about this, and decided to post a question on it. So say the FBI or SWAT has been tracking someone who has kidnapped a child, or something, and they corner him with the child he has abducted, except he has a gun to the childs head. (Or any scenario like that.) I seems like something like that could happen often, but what could they do? Thanks for your guy's help!