Choose the correct answer of the following question:

Question:

Choose the correct answer of the following question:

The lengths of a vertical rod and its shadow are in the ratio $1: \sqrt{3}$. The angle of elevation of the sun is

(a) 30°                    (b) 45°                     (c) 60°                     (d) 90°

 

Solution:

Let AB be the rod and BC be its shadow; and θθ be the angle of elevation of the sun.

We have,

$\mathrm{AB}: \mathrm{BC}=1: \sqrt{3}$

Let $\mathrm{AB}=x$

Then, $\mathrm{BC}=x \sqrt{3}$

In $\triangle \mathrm{ABC}$,

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

$\Rightarrow \tan \theta=\frac{x}{x \sqrt{3}}$

$\Rightarrow \tan \theta=\frac{1}{\sqrt{3}}$

$\Rightarrow \tan \theta=\tan 30^{\circ}$

$\therefore \theta=30^{\circ}$

Hence, the correct answer is option (a).

 

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