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.

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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.

Updated on 10-Oct-2022 13:28:12