Relieved means freed from worry at last. The result came, and it was not the bad one.
It takes to and a verb, or a that-clause: relieved to hear it, relieved that nobody was hurt. The word describes the moment after fear rather than happiness generally, which is why relieved and pleased are not the same. There is a separate physical sense from the verb relieve, meaning to take over from somebody on duty, so a sentry is relieved at midnight. Relieving pain means reducing it.
1adjectiverelievedNo longer anxious, because a feared outcome did not happen.
“He was hugely relieved to see the lights still on.”