A man sees the top of a tower in a mirror which is at a distance of 87.6m from the tower. The mirror is on the ground facing upwards. The man is 0.4m away from the mirror and his height is 1.5m.

How tall is the tower
How tall is the tower
Step 1: Examine the given figure and make a note of the given measurements
Step 2: Prove that the two triangles are similar by using the given data.
EXPLANATION: From the figure we get
\angle B = \angle D = 90 \degree
\angle BCA = \angle DCE
Because, angle of incidence and angle of reflection are same)
So, ∆ABC ~ ∆EDC ( by AAA Theorem)
Step 3: Use the AAA theorem to calculate unknown value
AAA THEOREM: In two triangles, if the angles are equal, then the sides
opposite to the equal angles are in the same ratio (or proportional) and hence
the two triangles are similar.
\frac{AB}{ED}=\frac{BC}{CD}
Step 4: Substitute the known values in the AAA theorem
EXAMPLE: \frac{1.5}{h}=\frac{0.4}{87.6}
h=\frac{1.5*87.6}{0.4}
h = 328.5 m
The height of the lamp post is 328.5 m