Question

Choose the correct answer of the following question:

If a pole 12 m high casts a shadow $4\sqrt{3}$ m long on the ground, then the sun's elevation is

(a) 60° (b) 45° (c) 30° (d) 90° [CBSE 2013C]

Answer 1

Let AB be the pole, BC be its shadow and $\theta$ be the sun's elevation.

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{AB}=12\mathrm{m}\mathrm{and}\mathrm{BC}=4\sqrt{3}\mathrm{m} \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{12}{4\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{3}{\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{3}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{3\sqrt{3}}{3} \\ \Rightarrow \tan \theta =\sqrt{3} \\ \Rightarrow \tan \theta =\tan 60° \\ \therefore \theta =60° \end{gathered}$$

Hence, the correct answer is option (a).