A vertical stick 10 cm long casts a shadow 8 cm long.

Question:

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.

Solution:

Now,

$\triangle \mathrm{ABC} \sim \Delta \mathrm{PQR}$  (AA Similarity)

$\frac{A B}{B C}=\frac{P Q}{Q R}$

$\frac{10 \mathrm{~cm}}{8 \mathrm{~cm}}=\frac{P Q}{30 \mathrm{~m}}$

$P Q=\frac{30 \mathrm{~m} \times 10 \mathrm{~cm}}{8 \mathrm{~cm}}$

$P Q=\frac{3000 \mathrm{~cm} \times 10 \mathrm{~cm}}{8 \mathrm{~cm}}$

$P Q=\frac{30000 \mathrm{~cm}}{8 \mathrm{~cm}}$

$=\frac{3750}{100}$

$=37.5 \mathrm{~m}$

Hence $P Q=37.5 \mathrm{~m}$

 

 

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