Question

A man stands vertically in front of a mirror. His eyes are 1.50 m above the floor, and the top of his head is 0.15 m higher. He wishes to know the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. What is the height above the floor of the BOTTOM of this mirror?

I need the steps and equation(s) to solving this problem, I already have the answer. Thanks!

Answer 1

Let us suppose that:-
A be the top of the man's head with reflection A',
B be the man's eyes with reflection B',
C be the man's feet with reflection C'.
MN be the wall (M at the top) on which the mirror is fixed.
Join A'B meeting MN at P (top of the required mirror),
and C'B meeting MN at Q (bottom of the required mirror).
As the image is as far behind the mirror as the man is in front,
tringles PQB and A'CB are similar, with the dimensions of the former being half
those of the latter.
Therefore:
QN = BC / 2 = 0.75 m.
PQ = A'C' / 2 = AC / 2 = 1.65 / 2 = 0.825 m.
PN = PQ + QN = 1.575 m.