Question : The ratio of the length of a rod and its shadow is $1: \sqrt{3}$. The angle of elevation of the sun is:
Option 1: $90^{\circ}$
Option 2: $30^{\circ}$
Option 3: $45^{\circ}$
Option 4: $60^{\circ}$
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Correct Answer: $30^{\circ}$
Solution :
The ratio of the length of a rod and its shadow, $\frac{AB}{BC} = \frac{1}{\sqrt{3}}$
⇒ $\tan \theta = \frac{AB}{BC}$
⇒ $\tan \theta = \frac{1}{\sqrt{3}}$
⇒ $\tan\theta = \tan 30^{\circ}$
⇒ $\theta =30^{\circ}$
Hence, the correct answer is $30^{\circ}$.
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