Question

Choose the correct answer of the following question:

The shadow of a 5-m-long stick is 2 m long. At the same time, the length of the shadow of a 12.5-m-high tree is

(a) 3 m (b) 3.5m (c) 4.5 m (d) 5 m [CBSE 2011]

Answer 1

Let AB be a stick and BC be its shadow; and PQ be the tree and QR be its shadow.

We have,

$$\begin{gathered} \mathrm{AB}=5\mathrm{m},\mathrm{BC}=2\mathrm{m},\mathrm{PQ}=12.5\mathrm{m} \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{5}{2}.....\left(\mathrm{i}\right) \\ \mathrm{Now},\mathrm{in}∆\mathrm{PQR}, \\ \tan \theta =\frac{\mathrm{PQ}}{\mathrm{QR}} \\ \Rightarrow \frac{5}{2}=\frac{12.5}{\mathrm{QR}}\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ \Rightarrow \mathrm{QR}=\frac{12.5\times 2}{5}=\frac{25}{5} \\ \therefore \mathrm{QR}=5\mathrm{m} \end{gathered}$$

Hence, the correct answer is option (d).