Step 1: Understand the question and note down the given data

From the figure:

Person's height AB = 1.65 m

The length of a person's shadow BC = 1. 8 m

The length of a lamp-post's shadow QR = 5.4 m

Lamp-post's height PQ = ?

Step 2: Prove that the two triangles are similar by using the given data.

From the figure we get

\angle B = \angle Q = 90 \degree

\angle C = \angle R, \angle A = \angle P

Because, AC || PR, all sun’s rays are parallel at any instance)

We understand the triangles are similar because all three corresponding angles are equal.

Thus, ∆ABC ~ ∆PQR ( by AAA Theorem)

Step 3: Calculating unknown length

The three pairs of corresponding sides are in the same proportion to each other since the triangles are similar.

\frac{AB}{PQ} = \frac{BC}{QR}

Substitute the known values in the above equation

\frac{1.65}{PQ} = \frac{1.8}{5.4}

PQ = \frac{5.4 * 1.65}{1.8}

PQ = 4.95 m

Hence, the height of the lamp post is 4.95 m