How to make <div> fill <td> height

I've looked through several posts on StackOverflow, but haven't been able to find an answer to this rather simple question.

I have an HTML construct like this:

<table>
  <tr>
    <td class="thatSetsABackground">
      <div class="thatSetsABackgroundWithAnIcon">
        <dl>
          <dt>yada
          </dt>
          <dd>yada
          </dd>
        </dl>
      <div>
    </td>
    <td class="thatSetsABackground">
      <div class="thatSetsABackgroundWithAnIcon">
        <dl>
          <dt>yada
          </dt>
          <dd>yada
          </dd>
        </dl>
      <div>
    </td>
  </tr>
</table>

What I need is for the div to fill the height of the td, so I can be able to position the div's background (the icon) at the bottom-right corner of the td.

How do you suggest I go about that?