Choose the correct answer of the following question:
Question:

Choose the correct answer of the following question:

If a l.5-m-tall girl stands at a distance of 3 m from a lamp post and casts a shadow of length 4.5 m on the ground, then the height of the lamp post is

(a) 1.5 m                      (b) 2 m                      (c) 2.5 m                      (d) 2.8 m

Solution:

Let AB be the lamp post; CD be the girl and DE be her shadow.

We have,

$\mathrm{CD}=1.5 \mathrm{~m}, \mathrm{AD}=3 \mathrm{~m}, \mathrm{DE}=4.5 \mathrm{~m}$

Let $\angle \mathrm{E}=\theta$

In $\Delta \mathrm{CDE}$,

$\tan \theta=\frac{\mathrm{CD}}{\mathrm{DE}}$

$\Rightarrow \tan \theta=\frac{1.5}{4.5}$

$\Rightarrow \tan \theta=\frac{1}{3} \quad \ldots \ldots$ (i)

Now, in $\triangle \mathrm{ABE}$,

$\tan \theta=\frac{\mathrm{AB}}{\mathrm{AE}}$

$\Rightarrow \frac{1}{3}=\frac{\mathrm{AB}}{\mathrm{AD}+\mathrm{DE}} \quad[\mathrm{U} \operatorname{sing}(\mathrm{i})]$

$\Rightarrow \frac{1}{3}=\frac{\mathrm{AB}}{3+4.5}$

$\Rightarrow \mathrm{AB}=\frac{7.5}{3}$

$\therefore \mathrm{AB}=2.5 \mathrm{~m}$

Hence, the correct answer is option (c).