question_answer

The angle of elevation of the top of a pillar at any point A on the ground is\[{{15}^{o}}\]. On walking 40 metres towards the pillar, the angle become\[{{30}^{o}}\]. The height of the pillar is [MP PET 2001]

A) 40 metres

B) 20 metres

C) \[20\sqrt{3}metres\]

D) \[\frac{40}{3}\sqrt{3}metres\]

Correct Answer: B

Solution :

Let h be the height of pillar \[OB=h\cot {{30}^{o}}\] and \[OA=h\cot {{15}^{o}}\] Þ  \[AB=OA-OB=h(\cot {{15}^{o}}-\cot {{30}^{o}})\] Þ  \[\,h=\frac{40}{\cot {{15}^{o}}-\cot {{30}^{o}}}\] = 20 metre.