A vertical stick of length 7.5 m casts a shadow 5 m long on the ground and at the same time a tower casts a shadow 24 m long.
A vertical stick of length 7.5 m 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.
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 $\triangle A B C$ and $\triangle P Q R$ we have:
$\angle A B C=\angle P Q R=90^{\circ}$
$\angle A C B=\angle P R Q$ (Angular elevation of the Sun at the same time)
Therefore, by AA similarity theorem, we get:
$\triangle A B C \sim \triangle P Q R$
$\Rightarrow \frac{A B}{B C}=\frac{P Q}{Q R}$
$\Rightarrow \frac{7.5}{5}=\frac{x}{24}$
$\Rightarrow x=\frac{7.5}{5} \times 24=36 \mathrm{~m}$
Therefore, PQ = 36 m
Hence, the height of the tower is 36 m.
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