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A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 m long. Determine the height of the tower.
Given:
A vertical stick 10 cm long casts a shadow 8 cm long.
A tower casts a shadow 30 m long.
To do:
We have to find the height of the tower.
Solution:
Length of the stick $= 10\ cm$.
Length of the stick’s shadow $= 8\ cm$.
Length of the tower’s shadow $= 30\ m = 30\times100\ cm=3000\ cm$.
In $ΔABC$ and $ΔPQR$
$\angle ABC = \angle PQR = 90^o$
$\angle ACB = \angle PRQ$ (Angular elevation of Sun is same)
Therefore,
$ΔABC ∼ ΔPQR$ (By AA similarity)
This implies,
$\frac{AB}{BC} = \frac{PQ}{QR}$ (Corresponding sides are proportional)
$\frac{10}{8} = \frac{PQ}{3000}$
$PQ = \frac{3000\times10}{8}$
$PQ = \frac{15000}{4}$
$PQ = 3750\ cm$
$PQ=\frac{3750}{100}\ m$
The height of the tower(PQ) is $37.5\ m$.