Question

You are 1.8 m tall and stand 2.8 m from a plane mirror that extends vertically upward from the floor. on the floor 1 m in front of the mirror is a table 0.8 m tall. what is the minimum height the mirror must have for you to be able to see the top of the table in the mirror

Answer 1

This problem must be solved using a sketch. I attached an illustration of the problem.
You must trace the ray that reflects from the top off the table to your eyes. This how eyesight works, light rays reflects off the objects into your eyes.
Law of reflection tells us that light ray reflects off the surface at the same angle in which it falls on it( i attached another illustration of this).
Now we can write tangens equations:
$tan(\theta)=\frac{h-0.8}{1}\\ tan(\theta)=\frac{1.8-h}{2.8}\\ \frac{h-0.8}{1}=\frac{1.8-h}{2.8}$
We solve for h:
$\frac{h-0.8}{1}=\frac{1.8-h}{2.8}\\ 2.8h-0.8\cdot 2.8=1.8-h\\ 3.8h=1.8+2.24\\ h=\frac{4.04}{3.8}\\ h=1.06m$