Question : The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar raised so that its angle of elevation at the same point may be 45°, is:
Option 1: 63.4
Option 2: 86.6
Option 3: 126.8
Option 4: 173.2
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Correct Answer: 63.4
Solution :
Given: The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°.
In $\triangle DBC$, $\tan 30°=\frac{DB}{BC}$
$⇒\frac{1}{\sqrt3}=\frac{DB}{150}$
$⇒DB=\frac{150}{\sqrt3}$
$⇒DB=50\sqrt3$
In $\triangle ABC$, $\tan45°=\frac{AB}{BC}$
$⇒1=\frac{AB}{150}$
$⇒AB=150$ m
Also, $AD = AB - DB$
$⇒AD=150 - 50\sqrt3$
$⇒AD=150-50\times 1.732$
$⇒AD=150-86.6$
$\therefore AD=63.4$ m
Hence, the correct answer is 63.4.
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