Question bank/JEE Main/Mathematics

Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and
CA = 6 m. A vertical lamp post at the mid point D of AC subtends an
angle 30º at B. The height (in m) of the lamp post is

A$\frac{3}{2}\sqrt{21}$B$2\sqrt{21}$C$\frac{2}{3}\sqrt{21}$D$7\sqrt{3}$

Show answer and solution▾

Length of median
$BM = \frac{1}{2}\sqrt{2\left( {BC}^{2} + {BA}^{2} \right) - (AC)^{2}} = \frac{1}{2}\sqrt{2(25 + 49) - 36}$
Let h be height of tower, given
$\tan 30^{\circ} = \frac{h}{2\sqrt{7}} \Rightarrow h = 2\sqrt{7/3} = \sqrt{28/3}$

Source: Grass-G / M-22 Mathematics Paper 19 Dec Eng.docx