Want to use inline-block?
In the title you specify display: inline-block.
We can do this and keep the sidebar fixed using calc(100% - 240px) to remove the sidebar width from the width of #content.
Having the divs like this: <div id="sidebar"></div><div id="content">fff</div> prevents an inline gap. More information here.
 
I have removed the scroll with height: calc(100% - 30px) on #container to remove the header height. Not critical enough for an old browser fallback.
 
Browser support: Of course, be aware of browser compatibility using calc() - IE 9 +. We can use an un-optimised fallback width for older browsers or, if really needed, I have included a basic jQuery calc() fallback that will set the width if calc() is not supported.
The jQuery fallback is from this answer. I added a width check so it will only run when the width is too small. This is particularly good if you include the jQuery library anyway.
Example
Note vertical-align: top to keep the inline-block divs positioned correctly vertically.
// calc fallback - optional
var checkWidth = $('#outer').width() - 240;
var contentWidth = $('#content').width();
if (checkWidth !== contentWidth) {
  alert('no calc :(');
  $('#content').css('width', '100%').css('width', '-=240px');
  $(window).resize(function() {
    $('#content').css('width', '100%').css('width', '-=240px');
  });
} else {
  alert('has calc :D !');  
}
* {
  box-sizing: border-box;
}
html,
body {
  margin: 0;
  padding: 0;
  height: 100%;
  width: 100%;
}
#Header {
  height: 30px;
  background-color: yellow;
}
#container {
  height: calc(100% - 30px);
  width: 100%;
}
#sidebar {
  background-color: orange;
  height: 100%;
  opacity: 0.3;
  width: 240px;
  display: inline-block;
  vertical-align: top;
}
#content {
  background-color: blue;
  height: 100%;
  width: calc(100% - 240px);
  display: inline-block;
  vertical-align: top;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div style="height: 100%" id="outer">
  <div id="Header"></div>
  <div id="container">
    <div id="sidebar"></div><div id="content">fff</div>
  </div>
</div>