JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Heights and Distances

Let the height of the shorter pole be $h$ meters, so the taller pole has height $3h$ meters. The poles are 150 m apart, so the observer at the midpoint is 75 m from each pole.

Let the angle of elevation to the shorter pole be $\theta$. Then the angle of elevation to the taller pole is $90°-\theta$ (complementary).

From the shorter pole: $\tan \theta =\frac{h}{75}$

From the taller pole: $\tan (90°-\theta )=\cot \theta =\frac{3h}{75}$

Since $\tan \theta \cdot \cot \theta =1$:



meters