Holy $h!t. I can't believe that someone who does any amount of construction type work - in any field - thought that was ok. I would hate to think what would happen if you fill the tub with water and put one or two people in it. If that was my house I wold box it the way guys explained above and I would install a post from underneath to provide additional support. Something like this
We haven't got enough information to get excited about it yet. I don't think any one asked what else is supported by that joist or how long it is.
The weight of the water and people in it does not count. On one side it will be sitting right above the good floor joist and on the other side it will be hung from the wall which is right above the other good floor joist.
Do not use flat bottom gables with scissor trusses.
I totally agree with the above comments. You NEVER just cut a floor joist for something as has been indicated. Regardless, whatever you decide for a "fix" I'd strongly suggest the addition of a tele-post (support post that is adjustable) … just to reinforce the area. It's over-kill but better than the alternative.