GeoGebra 2 - Right Triangles

Directions: Click and drag any blue point:

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

Now go back and find out how to make this and why it works!
 

LFS, Created with GeoGebra