[html] How to force child div to be 100% of parent div's height without specifying parent's height?

The easiest way to do this is to just fake it. A List Apart has covered this extensively over the years, like in this article from Dan Cederholm from 2004.

Here's how I usually do it:

<div id="container" class="clearfix" style="margin:0 auto;width:950px;background:white url(SOME_REPEATING_PATTERN.png) scroll repeat-y center top;">
    <div id="navigation" style="float:left;width:190px;padding-right:10px;">
        <!-- Navigation -->
    </div>
    <div id="content" style="float:left;width:750px;">
        <!-- Content -->
    </div>
</div>

You can easily add a header onto this design by wrapping #container in another div, embedding the header div as #container's sibling, and moving the margin and width styles to the parent container. Also, the CSS should be moved into a separate file and not kept inline, etc. etc. Finally, the clearfix class can be found on positioniseverything.