#### 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, find how far she is away from the base of the pole.

height of street light bulb = 6 m

woman's height = 1.5 m

Let the distance between pole and women = x m

$Here\ CD\parallel AB$

$In\ \Delta CDE$ $and$ $\Delta ABE$

$\angle E=\angle E$  $\text{(common angle)}$

$\angle ABE=\angle CDE$  $(\text{ each angle 90}^0)$

$\therefore \Delta CDE\sim \Delta ABE\text{ (by AA similarity criterion)}$

Then

$\frac{ED}{EB}=\frac{CD}{AB}$

$\\\frac{3}{3+x}=\frac{1.5}{6}\\3 \times 6=1.5\left ( 3+x \right )\\18=4.5+1.5x\\18-4.5=1.5x$

$\\\frac{13.5}{1.5}=x\\9m=x$