Question

A vertical pole of length 7.5 cm casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long. Find the height of the tower.

Answer 1

Let AB be the vertical stick and BC be its shadow.
Given:
AB = 7.5 m, BC = 5 m 

 Let PQ be the tower and QR be its shadow.
Given:
QR = 24 m
Let the length of PQ be x m.
In Δ ABC and Δ PQR, we have:
∠𝐴𝐵𝐶 = ∠𝑃𝑄𝑅 = 90° 
∠𝐴𝐶𝐵 = ∠𝑃𝑅𝑄 (Angular elevation of the sun at the same time)
Therefore, by A similarity theorem, we get:
Δ ABC ~ Δ PQR 

⇒`(AB)/(BC)=(PQ)/(QR)`

⇒ `7.5/5=x/24` 

x = ` 7.5/5xx24=36 cm` 

Therefore, PQ = 36 m
Hence, the height of the tower is 36 m.