I was greatly relieved at the result, for more than one reason.

The party was greatly relieved to get the whole business over and done with.

I told her the truth, and she seemed greatly relieved.

I was greatly relieved to find that it didn't take them long to change.

"She was greatly relieved to hear that you are well."

Wonderful, she thought, feeling greatly relieved after talking to him for only three minutes.

But everyone seemed greatly relieved to have any images at all.

Jim B. said he was greatly relieved to have done the right thing.

His men were greatly relieved when he returned to camp the next day.

In many ways I was greatly relieved as it had become obvious to me that he wasn't well.