Question

Choose the correct answer of the following question:

In the given figure, a tower AB is 20 m high and BC, its shadow on the ground is $20\sqrt{3}$ m long. The sun's altitude is

(a) 30° (b) 45° (c) 60° (d) none of these [CBSE 2015]

Answer 1

Let the sun's altitude be $\theta$.

We have,

$$\begin{gathered} \mathrm{AB}=20\mathrm{m}\mathrm{and}\mathrm{BC}=20\sqrt{3}\mathrm{m} \\ \mathrm{In}∆\mathrm{ABC}, \\ \tan \theta =\frac{\mathrm{AB}}{\mathrm{BC}} \\ \Rightarrow \tan \theta =\frac{20}{20\sqrt{3}} \\ \Rightarrow \tan \theta =\frac{1}{\sqrt{3}} \\ \Rightarrow \tan \theta =\tan 30° \\ \therefore \theta =30° \end{gathered}$$

Hence, the correct answer is option (a).