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Question
The height of the vertical pole is \[\sqrt{3}\] times the length of its shadow on the ground, then angle of elevation of the sun at that time is
Options
30º
60º
45º
75º
Solution
Let the angle of elevation of the sun be θ.
Suppose AB is the height of the pole and BC is the length of its shadow.
It is given that, AB = \[\sqrt{3}\]BC
In right ∆ABC,
\[\tan\theta = \frac{AB}{BC}\]
\[ \Rightarrow \tan\theta = \frac{\sqrt{3}BC}{BC} = \sqrt{3}\]
\[ \Rightarrow \tan\theta = \tan60°\]
\[ \Rightarrow \theta = 60°\]
Thus, the angle of elevation of the sun is 60º.
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