Sacrificing Hostage taker to cast a demon which I took hostage

So as you can guess, can I?

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Let’s say I have 8 mana and the enemy has a https://scryfall.com/card/m19/91/demon-of-catastrophes , I have no other creatures. Can I take it hostage and play it using the hostage taker as sacrifice, or will the hostage taker (as it is paid as cost) already leave the board and therefore stop me from actually casting the demon?