question_answer

A vertical stick 12m long casts a shadow 8m long on the ground. At the same time a tower casts the shadow 40m long on the ground. Then the height of the tower is:

A) 65 m

B) 60 m

C) 70 m

D) 72 m

Correct Answer: B

Solution :

[b] Let AB be the vertical stick and AC be its shadow. Also, let DE be the vertical tower and DF be its shadow. Join BC and EF. Let \[DE=xm\]

We have, \[AB=12m,\]\[AC=8m,\]and \[DF=40m.\]

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

We have, \[\angle A=\angle D=90{}^\circ \]

\[\angle C=\angle F\]  (Angular elevation of the Sun)

\[\therefore \,\,\,\Delta ABC\tilde{\ }\Delta DEF\](By AA similarity criterion)

\[\Rightarrow \,\,\,\,\,\frac{AB}{DE}=\frac{AC}{DF}\,\,\,\,\Rightarrow \,\,\,\frac{12}{x}=\frac{8}{40}\,\,\,\,\Rightarrow \,\,\,\frac{12}{x}=\frac{1}{5}\Rightarrow \,x=60m\]