SATHEE: Quantitative Aptitude Ques 1542

Quantitative Aptitude Ques 1542

Question: There is a flag staff on top of a building. The height of the building being 10 m. At a point certain distance away from the foot of the building the angles of elevation to the top and bottom of flag staff are $ 60{}^\circ $ and $ 30{}^\circ , $ respectively. Find the height of the flag staff.

Options:

A) 20 m

B) 5 m

C) 15 m

D) 25 m

Show Answer

Answer:

Correct Answer: A

Solution:

(a) Let AB be the height of the building and BC the height of the flag staff.
Then, $ AB=10m, $
$ \angle ADB=30{}^\circ , $ $ \angle ADC=60{}^\circ $ In right angled $ \Delta BAD, $ $ \tan 30{}^\circ =\frac{AB}{AD} $

$ \Rightarrow $ $ \frac{1}{\sqrt{3}}=\frac{10}{AD} $ In right angled $ \angle CAD $ $ \tan 60{}^\circ =\frac{AC}{AD}=\frac{AB+BC}{AD} $ $ \sqrt{3}=\frac{10+BC}{10\sqrt{3}} $ $ \sqrt{3}\times 10\sqrt{3}=10+BC $

$ \Rightarrow $ $ 10\times 3=10+BC $
$ \Rightarrow $ $ BC=20m $

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