A pole is situated at the centre of a regular hexagonal park. The angle of elevation of the top of the vertical pole when observed from each vertex of the hexagon is π 3 . If the area of the circle circumscribing the hexagon is 27 m 2 , then the height of the tower is

Step-by-step solution

Let a be the side of the regular hexagon Now, for the equilateral triangle F O A , we have O F = O A = A F = a Hence, area of circle, π a 2 = 27 ⇒ a = 3 3 π meters ... 1 In right-angled triangle A O T , right angled at O , we have t a n π 3 = O T O A ⇒ O T = O A   t a n π 3 ⇒ O T = 3 3 π × 3 ∴ O T = 9 π meters ∴ Height of the tower = 9 π meters.