Question

A light ray reflects from a mirror hanging vertically on a wall in your bathroom, and the ray strikes a particular point on the opposite wall (see figure below). The bottom end of the mirror is then tilted slightly away from the wall so that the mirror makes an angle of 4

Answer 1

It will be helpful to draw a diagram showing the incident and reflected rays after reflection.
From simple geometry the angle between the rays is (180 - 2 * 86) deg = 8 deg.
(Using the fact that the angle of incidence equals the angle of reflection)
The angle between the rays is twice that by which the mirror is tilted.
Then tan theta = S / L   where S is the deflection of the reflected ray and L the length of the room.
L = .49 / tan 8 = 3.49 meters