question_answer

Two pillars of equal height stand on either side of a roadway which is 60 metres wide. At a point in the roadway between the pillars, the elevation of the top of pillars are 60° and 30°. The height of the pillars is [UPSEAT 2004]

A) \[15\sqrt{3}m\]

B) \[\frac{15}{\sqrt{3}}m\]

C) \[15m\]

D) \[20m\]

Correct Answer: A

Solution :

  \[\tan 60{}^\circ =\frac{h}{x}\Rightarrow \frac{\sqrt{3}}{1}=\frac{h}{x}\Rightarrow h=\sqrt{3}x\]                     .....(i)      \[\tan 30{}^\circ =\frac{h}{60-x}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{60-x}\Rightarrow 60-x=\sqrt{3}h\] .....(ii) From equation (i) and (ii), \[60-x=\sqrt{3}(\sqrt{3}x)\]   \[\frac{60}{4}=x\Rightarrow x=15\] Then \[h=\sqrt{3}x\Rightarrow h=15\sqrt{3}\] metre.