嵌入具有正确宽高比的Youtube / Vimeo视频

So I have a video page where I embed a vimeo video. The trouble is, the aspect ratio is often wrong because I don't set the width and height. Leaving me with black bars on the video. I only pass in the vimeo ID dynamically, so I don't set a width and height per video. So I have a video page where I embed a vimeo vi