Question : The angle of elevation of the top of the pillar from the foot and the top of a building 20 m high, are 60° and 30°, respectively. The height of the pillar is:
Option 1: $10$ m
Option 2: $10\sqrt{3}$ m
Option 3: $60$ m
Option 4: $30$ m
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Correct Answer: $30$ m
Solution :
Let, AB = height of pole = $h$ m
CD = height of building = 20 m = BE
$\angle$ADB = 60°; $\angle$ACE = 30°
Let, AE = $x$ m; BD = EC = $y$ m
In ∆ ABD, $\tan 60° =\frac{AB}{BD}$
⇒ $\sqrt{3}=\frac{x+20}{y}$
⇒ $x+20=\sqrt{3} y$ ---(1)
In ∆ AEC, $\tan 30°=\frac{AE}{EC}$
⇒ $\frac{1}{\sqrt{3}}=\frac{x}{y}$
⇒ $y=\sqrt{3}x$ ----(2)
Putting the value of $y$ in equation 1 we get,
$x+20=\sqrt{3}×\sqrt{3}x$
⇒ $2x=20$
⇒ $x=10$ m
So, AB = $x+20=10+20=30$ m
So, the height of the pole is 30 m.
Hence, the correct answer is $30$ m.
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