ため息をつく (let out a sigh)

Letting out a grand sigh, they thump the bread down on the table and plop into a chair.

She sighed at her unhappy fate.

She heaved a sigh of relief when work was over.

She let out a sigh and clenched both hands tightly.

Perhaps sensing he couldn't be persuaded, Kurosaki-sensei sighed and took his seat.