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  • A vertical stick which is 18 cm long casts a 12-cm-long shadow on the ground. At the same time, a vertical tower casts a 50-m-long shadow on the ground. Find the height of the tower<div class='

A vertical stick which is 18 cm long casts a 12-cm-long shadow on the ground. At the same time, a vertical tower casts a 50-m-long shadow on the ground. Find the height of the tower

Option: 1

75 m


Option: 2

62.5 m


Option: 3

82.5 m


Option: 4

None of the above


Answers (1)

best_answer

Let AB be the vertical stick and let AC be its shadow.

Then, AB = 18 m AC = 12 m

Let DE be the vertical tower and let DF be its shadow.

Then, DF = 50 m.

Let DE x = m.

Now, in \triangle BAC\text{ and }\triangle EDF

we have

\\\angle B A C=\angle E D F=90^{\circ} \\ \\\angle A C B=\angle D F E\qquad\text{[angular elevation of the sun at the same time] }

\\\therefore \quad \triangle B A C \sim \triangle E D F \\ \\\Rightarrow \quad \frac{A B}{D E}=\frac{A C}{D F} \Rightarrow \frac{18}{x}=\frac{12}{50} \\ \\\Rightarrow \quad x=\frac{(18 \times 50)}{12}=75

Hence, the height of the tower is 75 m.

Posted by

mansi

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