how do I give a div a responsive height

For the height of a div to be responsive, it must be inside a parent element with a defined height to derive it's relative height from.

If you set the height of the container holding the image and text box on the right, you can subsequently set the heights of its two children to be something like 75% and 25%.

However, this will get a bit tricky when the site layout gets narrower and things will get wonky. Try setting the padding on .contentBg to something like 5.5%.

My suggestion is to use Media Queries to tweak the padding at different screen sizes, then bump everything into a single column when appropriate.

I know this is a little late to the party but you could use viewport units

From caniuse.com:

Viewport units: vw, vh, vmin, vmax - CR Length units representing 1% of the viewport size for viewport width (vw), height (vh), the smaller of the two (vmin), or the larger of the two (vmax).

Support: http://caniuse.com/#feat=viewport-units

div {
/* 25% of viewport */
  height: 25vh;
  width: 15rem;
  background-color: #222;
  color: #eee;
  font-family: monospace;
  padding: 2rem;
}

<div>responsive height</div>