You can do this with position:absolute; on the #second div like this :
CSS :
#wrapper{
position:relative;
}
#second {
position:absolute;
top:200px;
bottom:0;
left:0;
width:300px;
background-color:#9ACD32;
}
EDIT : Alternative solution
Depending on your layout and the content you have in those divs, you could make it much more simple and with less markup like this :
HTML :
<div id="wrapper">
<div id="first"></div>
</div>
CSS :
#wrapper {
height:100%;
width:300px;
background-color:#9ACD32;
}
#first {
background-color:#F5DEB3;
height: 200px;
}