The fear of heights, also known as acrophobia, is indirectly irrational. This is because the fear itself is not caused by heights...rather, the fear is caused by the irrational thoughts you have about heights. So it is your thoughts about the heights that are irrational, such that you may think you are in danger, or that harm will come to you, and that you can't cope. It is these irrational thoughts that leads to the fear.
The following video explains about how irrational thoughts cause anxiety and fear, and what you can do to address it: