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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.
Solution
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:
∠๐ด๐ต๐ถ = ∠๐๐๐
= 90°
∠๐ด๐ถ๐ต = ∠๐๐
๐ (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.
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