Question : A person standing at a distance looks at a building having a height of 1000 metres. The angle between the top of the building and the ground is 30o. At what approximate distance (in metres) is the person standing away from the building?
Option 1: 1000
Option 2: 936
Option 3: 1732
Option 4: 1542
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Correct Answer: 1732
Solution :
Given:
AB = Height of the building = 1000 metres
Let the distance of the man from the building, BC be $x$.
From $\triangle$ ABC, we get
$\tan 30° = \frac{AB}{BC}$
⇒ $\frac{1}{\sqrt{3}}= \frac{1000}{x}$
⇒ $ x = 1000\sqrt{3}$
⇒ $x$ = 1000 × 1.732
So, the distance of the man from the building is 1732 metres.
Hence, the correct answer is 1732.
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