RRB Technician 2014 Ques 9
Question: If a flag-staff of 6 m high placed on the top of a tower throws a shadow of $ 2\sqrt{3}m $ along the ground, then the angle that the Sun makes with the ground is
Options:
A) $ 60^{o} $
B) $ 30^{o} $
C) $ 90^{o} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- Let OA and AB be the shadows of tower OR and flag-staff TO respectively on the grounds. Let the Sun makes an angle ^ with the ground. Let $ OA=x $ In right angled $ \Delta AOR, $ $ \tan \phi =\frac{h}{x} $ …(i) and in $ \Delta BOQ. $ $ \tan \phi =\frac{h+6}{x+2\sqrt{3}} $ …(ii) From Eqs. (i) and (ii), $ \frac{h}{x}=\frac{h+6}{x+2\sqrt{3}} $
$ \Rightarrow $ $ h(x+2\sqrt{3})=x(h+6) $
$ \Rightarrow $ $ 2\sqrt{3}h=6x $
$ \Rightarrow $ $ x=\frac{h}{\sqrt{3}} $
$ \therefore $ $ \tan \phi =\frac{h}{x}\Rightarrow \tan \phi =\sqrt{3} $
$ \Rightarrow $ $ \phi =60^{o} $
BETA
