Question
A vertical stick 10cm long casts a shadow 8cm long. At the same time a tower casts a shadow 30m long. Determine the height of the tower.
✓
Answer
Length of stick = 10cmLength of shadow of stick = 8cm
Length of shadow of tower = h cm
In $\triangle\text{ABC}$ and $\triangle\text{PQR}$
$\angle\text{B}=\angle\text{Q}=90^\circ$
And, $\angle\text{C}=\angle\text{R}$ [Angular elevation of sum]
Then, $\triangle\text{ABC}\sim\triangle\text{PQR}$ [By AA similarity]
$\therefore\frac{\text{AB}}{\text{PQ}}=\frac{\text{BC}}{\text{QR}}$
$\Rightarrow\frac{10\text{cm}}{8\text{cm}}=\frac{\text{h cm}}{3000}$
$\Rightarrow\text{h}=\frac{10}{8}\times3000=3750\text{cm}=37.5\text{m}$
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