A man who is $6$ ft tall is standing in front of a plane mirror that is $2$ ft in length. The mirror is placed lengthwise with its bottom edge $4$ ft above the floor on a wall that is $5$ ft away(Assume that his eyes are right at the top of his head).
1) How much of his image (i.e. what length of himself) can the man see?
2) How much of the $8$ ft-tall tree behind him, $10$ ft away from the wall, can he see?
3) When the man moves to stand next to the tree, with the mirror staying in place, how much of himself can he now see? How much of the tree can he now see?
Attempt:1) I know about the $2:1$ rule so since the mirror is $2$ ft long he must be able to see the upper four ft of his body. Does the distance from the mirror matter though?
2) He should not be able to see the tree because he himself is covering it. I am not sure about that. Hints please.
3)The answers will be the same as in two previous questions. Again I am really not sure about that. An intuitive explanation or hint would be great. Thanks.