JEE Main 2021 (Online) 4th August Morning ShiftQuestion 1
Ten vertical poles of different height standing at equal distances on a straight line, subtend the same angle $30^{\circ}$ at a point $O$ on the line. If the height of the tallest pole is $12$ units and the distance of the foot of the shortest pole from $O$ is $1$ unit, then the distance between two consecutive poles is
Trigonometric Ratio & Identities
Solution
Concept. Each top is seen at $30^\circ$, so height $=\frac{\text{distance}}{\sqrt3}$; the distances form an A.P. Formulas used. (1) $h=d\tan30^\circ=\frac{d}{\sqrt3}$Step 1 - Farthest pole. The tallest pole ($h=12$) is the farthest: $d=12\sqrt3$. Step 2 - Nearest pole. The shortest pole is at $d=1$. Step 3 - Gap. Ten poles make $9$ equal gaps: $\dfrac{12\sqrt3-1}{9}$. Answer: (A)