A lamp post standing at a point A on a circular path of radius r subtends an angle α at some point B on the path, and AB subtends an angle of 45∘ at any other point on the path, the height of the lamp post is
A
√2rcotα
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B
r√2tanα
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C
√2rtanα
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D
r√2cotα
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Solution
The correct option is C√2rtanα
Let AM is the lamp post at point A of height h.
ABsubtends an angle of 45∘ at any point on the circle. Therefore it will subtend an angle of 90∘ at the center.
So, we can say that △OAB is a right-angled triangle with a right angle at O.