Create interactive search filter
What you are looking for is hierarchical list and can be accomplished by using these well-maintained modules below. The difference is Simple Hierarchical Select module provides a simpler implementation for dependent taxonomies [might work for your situation better]. 


  - Hierarchical select -- 
  This module defines the "hierarchical_select" form element, which is a greatly enhanced way for letting the user select items in a hierarchy. Hierarchical Select has the ability to save the entire lineage of a selection or only the "deepest" selection. You can configure it to force the user to make a selection as deep as possible in the tree, or allow the user to select an item anywhere in the tree. Levels can be labeled, you can configure limit the number of items that can be selected, configure a title for the dropbox, choose a site-wide animation delay, and so on. You can even create new items and levels through Hierarchical Select!
  
  Simple hierarchical select Simple hierarchical select defines a new form widget for taxonomy fields to select a term by "browsing" through the vocabularies hierarchy.
  The widget is available in node forms and as Views exposed filter.This module has been inspired by Hierarchical select but is much simpler (hence the name ;) ).Unlike Hierarchical select this module provides a simple widget for taxonomy terms only. As an addition Simple hierachical select works as Views exposed filter.