Different levels of bowing
Bowing is customary in many Asian countries, from Japan to Taiwan and even Indonesia to some extent. However, Japan takes its bowing game to different levels. There’s a type of bow that you do when you meet a friend, and another one when meeting a superior.
The general rule is that you should bend the top part of your body 15 degrees forward when greeting a friend and 30 degrees when greeting a senior or a person of power. However, nobody keeps a protractor on hand, so just make sure that you bow a little deeper when greeting your boss.