Quantitative Aptitude Ques 1825
Question: A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is $ 60{}^\circ . $ When he retires 80 m from the corner, along the same straight line, he finds the angle to be $ 30{}^\circ . $ The length of the field is
Options:
A) $ 20m $
B) $ 40\sqrt{2}m $
C) $ 40m $
D) $ 20\sqrt{2}m $
Show Answer
Answer:
Correct Answer: C
Solution:
- Let the length of football field be $ lm. $ From the figure, Height of the pole $ =xm $
$ \therefore $ In $ \Delta ABC, $ $ \tan 60{}^\circ =\frac{x}{l} $
$ \Rightarrow $ $ \sqrt{3}=\frac{x}{l} $
$ \Rightarrow $ $ x=\sqrt{3}l $ … (i)
Now, in $ \Delta ABD $
$ \tan 30{}^\circ =\frac{x}{l+80} $
$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{x}{l+80} $
$ \Rightarrow $ $ l+80=\sqrt{3}x $ Now, from Eq. (i), we get $ l+80=\sqrt{3},(\sqrt{3}l) $
$ \Rightarrow $ $ l+80=3l $
$ \Rightarrow $ $ 80=3l-l $
$ \Rightarrow $ $ l=\frac{80}{2}=40m $
BETA
