In a recent storm two large branches broke off of my tree. They broke off right at the trunk, so I can't cut it back further to make it a clean cut. is there anything I should do to help protect the rest of the tree?
EDIT: Here are some pictures that were requested:
The tree is in Southwest Ohio, near Cincinnati.
Tree as a whole. You can see essentially the whole back half came down. From the front of the tree though it still looks good.
Side view of the broken section so you can get a better idea of how thick the tree is there: (Couldn't get a good side view because other branches were in the way.)