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