Q18 of 61 Page 215

The angle of elevation of a hovering helicopter as seen from a point 45 m above a lake is 30° and the angle of depression of its reflection in the lake, as seen from the same point and at the same time, is 60°. Find the distance of the helicopter from the surface of the lake.


Given, ED = 45 m and DF = ?


Let EF = x, DF = h


⇒ DC = h (∵ height of reflection = height of object)


In a right triangle FAE,


We know,





AE = (h – 45) √3 ……… (1)


And, in right triangle ACE,





………(2)


Now, ∵BC = AD


⇒ equation (1) = equation (2)



⇒ 3(h – 45) = 45 + h


⇒ 3h – 135 = 45 + h


⇒ 2h = 45 + 135


⇒ 2h = 180


⇒ h = 90 m


∴ the distance of the helicopter from the surface of the lake is


90 m.


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