"The sun rises in the east." Is 'rises' a transitive verb or intransitive verb?
It is an intransitive verb. See explanation.
A transitive verb is a verb which can (sometimes must) have an object. An example could be verb to write.
When you use this verb you often (if not always) add an object:
Henry wrote a letter.
A letter is the object of verb to write.
The verb rise is an intransitive one because there can be no object in a sentence using to rise.