question_answer

A flag pole 18 m high casts a shadow 9.6m long. Then, the distance of the top of the pole from the far end of the shadow is

A) 18m

B) 26m

C) 21m

D) 20.4m

Correct Answer: D

Solution :

Let BC= 18m be the flag pole and its shadow be AB = 9.6 m. The distance of the top of the pole, C from the far end i.e. A of the shadow is AC.

In right angled \[\Delta ABC\], \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

[by Pythagoras theorem]

\[\Rightarrow A{{C}^{2}}={{\left( 9.6 \right)}^{2}}+{{\left( 18 \right)}^{2}}\]

\[A{{C}^{2}}=92.16+324\]

\[\Rightarrow A{{C}^{2}}=416.16\]

\[\therefore AC=\sqrt{416.16}=20.4m\]

Hence, the required distance is 20.4 m.