Heres what you do in a nutshell. if you use plex already skip this.
1. download install plex media server and set it up using folders with your videos to add to the que.
2. the above might just work with Myplex.com but I have both. So get a my plex account and link your plex server/files to it.
3. install the plex chrome extension.
4. go to myplex account and your library. que up a video and start playing, cast it to chrome then hit full screen on the plex player. your audio and video will automatically size and cast to the tv. how awesome is that?