Half the height of the man : 1.50 m / 2 = 75 cm.
See the diagram .
There is a wall and the mirror is on it. The man and the mirror are standing vertically on the floor. The distance between them does not matter, as it is a plane mirror.
The rays from the head can be seen only if the mirror is positioned at the level of eyes. The rays from the feet can be visible after reflection from the mirror at the height of h/2, where h is the height of the person.
The mirror part, which is purple colored of height h/2 and positioned h/2 height above ground, is needed. This is the shortest mirror, for the person to be able to see his full image.