A vertical pole stands at a point A on the boundary of a circular park of radius ‘a’ and subtends an angle β at another point B on the boundary. If the chord AB subtends an angle α at the center of the park, the height of the pole is

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2asin⁡α2tan⁡β

2acos⁡α2tan⁡β

2asin⁡α2cot⁡β

2acos⁡α2cot⁡β

answer is A.

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Detailed Solution

Suppose that h be the height of the pole from triangle APB,tan⁡β=hAB⇒h=ABtan⁡β from triangle ABC,sin⁡α2=AB2a⇒AB=2asin⁡α2∴h=2asin⁡α2tan⁡β

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