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

Answer 1

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

We have,

$$\begin{gathered} \mathrm{CD}=1.5\mathrm{m},\mathrm{AD}=3\mathrm{m},\mathrm{DE}=4.5\mathrm{m} \\ \mathrm{Let}\angle \mathrm{E}=\theta \\ \mathrm{In}∆\mathrm{CDE}, \\ \tan \theta =\frac{\mathrm{CD}}{\mathrm{DE}} \\ \Rightarrow \tan \theta =\frac{1.5}{4.5} \\ \Rightarrow \tan \theta =\frac{1}{3}.....\left(\mathrm{i}\right) \\ \mathrm{Now},\mathrm{in}∆\mathrm{ABE}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{AE}} \\ \Rightarrow \frac{1}{3}=\frac{\mathrm{AB}}{\mathrm{AD}+\mathrm{DE}}\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ \Rightarrow \frac{1}{3}=\frac{\mathrm{AB}}{3+4.5} \\ \Rightarrow \mathrm{AB}=\frac{7.5}{3} \\ \therefore \mathrm{AB}=2.5\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (c).