One to one correspondence between metrics on vector bundles and $O(n)$ reductions

Question

During our lecture our professor said that there exists a one to one correspondence between metrics on a vector bundle $E\to M$ and $O(n)$ reductions. He said it is a good exercise to try and prove this, however I don't quite know how to start... Well for one way I thought, we can take in $O(n)$ trivializations the standard metric, and patch them up to a global one using partition of unity. But I am not sure if that is what is meant to do.