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