Question

A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height. 1.5 m casts a shadow of 3m, then find how far she is away from the base of the pole.

Answer 1

Let A be the position of the street bulb fixed on a pole AB = 6m and CD = 5m be the height of a woman and the shadow be ED = 3m. let distances between pole and woman be x m.

Here, woman and pole both are standing vertically,
So, CD II AB
In $\Delta CDE$ and $\Delta ABE$, $\angle E=\angle E$ [common angle]
$\angle ABE=\angle CDE$ [each equal to ${90}^{\circ }$]
$\therefore$ $\Delta CDE\sim \Delta ABE$ [by AAA similarity criterion]
Then, $\frac{ED}{EB}=\frac{CD}{AB}$
$\Rightarrow$ $\frac{3}{3+x}=\frac{1.5}{6}$
$\Rightarrow$ $3\times 6=1.5(3+x)$
$\Rightarrow$ $18=1.5\times 3+1.5x$
$\Rightarrow$ $1.5x=18-4.5$
$\therefore$ $x=\frac{13.5}{1.5}=9m$
Hence, she is at the distance of 9m from the base of the pole.