Exams › SSC CGL (Prelims) › General

A flagstaff 5 metres high stands on top of a pedestal. From a point on the ground, the angle of elevation to the top of the flagstaff is \(60^\circ\), while the angle of elevation to the top of the pedestal from the same point is \(45^\circ\). Determine the height of the pedestal.

1. 2.5(\sqrt{3}-1) m
2. 5(\sqrt{3}-1) m
3. 2.5(\sqrt{3}+1) m
4. 5(\sqrt{3}+1) m

Correct answer: 2.5(\sqrt{3}+1) m

Solution

If the pedestal height is \(h\) and the distance from the observation point is \(d\), then \(\tan 45^\circ=h/d=1\), so \(d=h\). Also, \(\tan 60^\circ=(h+5)/d=\sqrt{3}\). Substituting \(d=h\) gives \(h+5=h\sqrt{3}\), hence \(h=\frac{5}{\sqrt{3}-1}=2.5(\sqrt{3}+1)\).

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