Question

Question 8
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 = 1.5m be the height of a woman and the shadow be ED = 3m. Let the distance 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, $\frac{ED}{EB}=\frac{CD}{AB}$
$\Rightarrow$ $\frac{3}{3+x}=\frac{1.5}{6}=\frac{1}{4}$
$\Rightarrow$ $3\times 4=3+x$
$\Rightarrow$ $12=3+x$
$\therefore$ $x=9m$
Hence, she is at the distance of 9m from the base of the pole.