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Question
If the height of a vertical pole is 3–√3 times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is
(A) 30°
(B) 60°
(C) 45°
(D) 75°
Solution
Let AO be the pole and OB be its shadow.
Let the length of the shadow be x.
Let θ be the angle of elevation of the Sun at that time.
Given:
Height of pole (h) =\[\sqrt{3} \times\] Length of its shadow
We have:
\[\tan \theta = \frac{AO}{OB}\]
\[ = \frac{h}{x}\]
\[ = \frac{\sqrt{3}x}{x}\]
\[ = \sqrt{3}\]
\[ \Rightarrow \tan \theta = \tan 60^o\]
\[ \Rightarrow \theta = {60}^\circ\]
Thus, the angle of elevation of the Sun is 60°.
Hence, the correct option is B.
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