How to reconnect left hinge to the rest of the hinge?

It's hard to tell from the picture how exactly the hinge has broken or if it would be repairable. If the screws have come loose but all of the actual hardware is still in tact then you make be able to use it. Otherwise, you might have to remove the display, remove the display hinge, and fully replace that particular broken hinge (which I believe also includes the display cable). Here's a guide for how to do that on the 13-inch model, which I think is a similar procedure for the 15-inch. Good luck!