Quantitative Aptitude Ques 983

Question: From a point A on the ground, the angle of elevation of the top of a 20 m tall building is $ 45{}^\circ . $ A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from A is $ 60{}^\circ . $ Find the length of flag staff.

Options:

A) 15.23 m

B) 14.64 m

C) 14 m

D) 15.65 m

Show Answer

Answer:

Correct Answer: B

Solution:

  • Given, BC = 20 m
    $ \angle BAC=45{}^\circ $ and $ \angle DAC=60{}^\circ $ In $ \Delta BAC, $ $ \tan 45{}^\circ =\frac{BC}{AC} $

$ \Rightarrow $ $ AC=20m $ In $ \Delta DAC, $ $ \tan 60{}^\circ =\frac{DC}{AC}=\frac{x+20}{20} $
$ \Rightarrow $ $ \sqrt{3}=\frac{x+20}{20} $

$ \Rightarrow $ $ x=20\sqrt{3}-20 $ $ =34.64-20=14.64m $

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