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
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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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