JEE Main & Advanced
Mathematics
Trigonometric Equations
Question Bank
Height and Distance
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.