question_answer

A vertical stick 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts a shadow 50m long on the ground. The height of the tower is

A) 100m

B) 120m

C) 25m

D) 200m

Correct Answer: A

Solution :

Let the height of the tower be x. As \[\angle B=\angle E=90{}^\circ\]and angle of elevation of sun is same.

In \[\Delta ABC\]and \[\Delta DEF\]

\[\angle B=\angle E\]                   [right angle]

\[\angle C=\angle F\]                   [angle of elevation]

\[\Delta ABC\tilde{\ }\Delta DEF\] [from AA similarity]

\[\therefore \,\,\,\,\frac{AB}{DE}=\frac{BC}{EF}\Rightarrow \,\frac{20}{x}=\frac{10}{50}\]

\[\Rightarrow \,\,\,\,\,x=\frac{20\times 50}{10}=100\,m\]