A pole stands vertically inside a triangular park ABC. Let the angel of elevation of the top of the pole from each corner of the park be π/3. If the radius of the circumcircle of ?ABC is 2, then the height of the pole is equal to :

Option 1 - 1/√3

Option 2 - √3

Option 3 - 2√3

Option 4 - 2√3/3

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Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 3

Detailed Solution:

Given a right-angled triangle with one angle π/3 (or 60°), and the side adjacent to it is h/2.
Using the tangent function: tan (π/3) = opposite / adjacent.
Let the adjacent side be 2. Then tan (π/3) = h/2.
We know tan (π/3) = √3.
So, h/2 = √3, which implies h = 2√3.