Set div height to fit to the browser using CSS

You could also use viewport percentages if you don't care about old school IE.

height: 100vh;

Setting window full height for empty divs

1st solution with absolute positioning - FIDDLE

.div1 {
  position: absolute;
  top: 0;
  bottom: 0;
  width: 25%;
}
.div2 {
  position: absolute;
  top: 0;
  left: 25%;
  bottom: 0;
  width: 75%;
}

2nd solution with static (also can be used a relative) positioning & jQuery - FIDDLE

.div1 {
  float: left;
  width: 25%;
}
.div2 {
  float: left;
  width: 75%;
}

$(function(){
  $('.div1, .div2').css({ height: $(window).innerHeight() });
  $(window).resize(function(){
    $('.div1, .div2').css({ height: $(window).innerHeight() });
  });
});