A person 1.65 m tall casts 1.8 m shadow. At the same instance, a lamp-post casts a shadow of 5.4 m. Find the height of the lamppost

Step 1: Understand the question and note down the given data
Step 2: Prove that the two triangles are similar by using the given data.
EXPLANATION: From the figure we get
\angle B = \angle Q = 90 \degree
\angle C = \angle R
Because, AC || PR, all sun’s rays are parallel at any instance)
So, ∆ABC ~ ∆PQR ( 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}{PQ} = \frac{BC}{QR}
Step 4: Substitute the known values in the AAA theorem
EXAMPLE: \frac{1.65}{PQ} = \frac{1.8}{5.4}
PQ = \frac{5.4 * 1.65}{1.8}
PQ = 4.95 m
The height of the lamp post is 4.95 m