Building A Battery

Start on move 37. Time is definitely a factor in this game but it doesn't change the fact that Mackenzie is about to use a strong attacking tecnique to change a back and forth game to certain checkmate. Over the next several moves Mackenzie is going to build his battery by stacking his rook and his queen. This tecnique and cliffs mistake in move 39 are going to allow kenzie to set up a game ending mating net. What move would you have made on 39 if you were black?