Just don’t set the height property in HighCharts and it will handle it dynamically for you so long as you set a height on the chart’s containing element. It can be a fixed number or a even a percent if position is absolute.
Highcharts docs:
By default the height is calculated from the offset height of the
containing element
Example: http://jsfiddle.net/wkkAd/149/
#container {
height:100%;
width:100%;
position:absolute;
}