This question was asked to my friend in an interview. You are provided a ladder and are led to a wall. The ladder must be kept against the wall making an angle of $45^\circ$ with the floor. You are given no measuring instruments whatsoever. All you have is yourself and the ladder.Nothing else. You are not given the value of the ladder's length or anything else of that sort.
How will you go about doing it?
If you think this involves physics rather than just math, please do mention if I must move the question elsewhere. And in case you're thinking, the interviewer has measuring instruments and will check your work after you're done.An exact value of $45^\circ$ is expected. And I am not sure if "not possible" or "insufficient data" is an accepted answer.
I really don't know what tags to use for this. I request you to edit my question with the appropriate tags.