JEE Main & Advanced
Mathematics
Trigonometric Equations
Question Bank
Height and Distance
question_answer
A vertical pole (more than 100 m high) consists of two portions, the lower being one-third of the whole. If the upper portion subtends an angle \[{{\tan }^{-1}}\frac{1}{2}\] at a point in a horizontal plane through the foot of the pole and distance 40 ft from it, then the height of the pole is [AMU 1981]
A)100 ft
B)120 ft
C)150 ft
D)None of these
Correct Answer:
B
Solution :
Obviously, from figure \[\tan \alpha =\frac{h/3}{40}=\frac{h}{120}\] .....(i) \[\tan \beta =\frac{h}{40}=\frac{3h}{120}\] .....(ii) Therefore \[\tan \theta =\tan (\beta -\alpha )\] \[\Rightarrow \] \[\frac{1}{2}=\frac{\frac{3h}{120}-\frac{h}{120}}{1+\frac{3{{h}^{2}}}{14400}}\Rightarrow h=120,\,40\] But \[h=40\] cannot be taken according to the condition, therefore\[h=120ft\].