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A street light bulb is fixed on a pole $ 6 \mathrm{~m} $ above the level of the street. If a woman of height $ 1.5 \mathrm{~m} $ casts a shadow of $ 3 \mathrm{~m} $, find how far she is away from the base of the pole.
Given:
A street light bulb is fixed on a pole \( 6 \mathrm{~m} \) above the level of the street.
A woman of height \( 1.5 \mathrm{~m} \) casts a shadow of \( 3 \mathrm{~m} \).
To do:
We have to find how far she is away from the base of the pole.
Solution:
Let $\mathrm{A}$ be the position of the street bulb fixed on a pole $A B=6 \mathrm{~m}$ and $C D=1.5 \mathrm{~m}$ be the height of the woman and her shadow be $\mathrm{ED}=3 \mathrm{~m}$.
Let the distance between the pole and the woman be $x \mathrm{~m}$.
Here,
$C D \| A B$
In $\triangle C D E$ and $\triangle A B E$,
$\angle E =\angle E$ (Common angle)
$\angle A B E =\angle C D E=90^{\circ}$
Therefore, by AA similarity,
$\triangle C D E \sim A B E$
This implies,
$\frac{E D}{E B}=\frac{C D}{A B}$
$\frac{3}{3+x}=\frac{1.5}{6}$
$3 \times 6=1.5(3+x)$
$18=1.5(3)+1.5 x$
$1.5 x=18-4.5$
$x=\frac{13.5}{1.5}$
$x=9 \mathrm{~m}$
Hence, she is at a distance of $9 \mathrm{~m}$ from the base of the pole.