I don't think he's breathed an outward sigh of relief.

I breathed a huge sigh of relief.

When Hooper got up we all breathed a sigh of relief.

Personally, I think everyone on the Lakeshore Committee breathed a sigh of relief once this project was completed. Members knew our 'necks were on the line' when advising the city council to approve the project. And it barely passed the city council by one vote.

It's a deep sigh of relief.

To have this over is a big sigh of relief.