Question : If the angle of elevation of the top of a pillar from the ground level is raised from 30° to 60°, the length of the shadow of a pillar of height $50\sqrt{3}$ metres will be decreased by:
Option 1: 60 metres
Option 2: 75 metres
Option 3: 100 metres
Option 4: 50 metres
Correct Answer: 100 metres
Solution :
Height of the pillar, $AB$ = $50\sqrt{3}$ metres
For the length of the shadow at an angle of elevation of 30°,
$\frac{50\sqrt{3}}{BC} = \tan 30°$
⇒ $\frac{50\sqrt{3}}{BC} = \frac{1}{\sqrt{3}}$
⇒ $BC = 150$ metres
For the length of the shadow at an angle of elevation of 60°,
$\frac{AB}{BD} = \tan 60°$
⇒ $\frac{50\sqrt{3}}{BD} = \sqrt{3}$
⇒ $BD = 50$ metres
Final decrement in the length of shadow = $BC-BD$
= 150 – 50
= 100 metres
Hence, the correct answer is 100 metres.
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