Question

From a point $100m$ above a lake the $Le$ of a stationary helicopter is $30$ and $Ld$ of reflection of the helicopter in the lake is ${60}^{\circ }$. Find height of helicopter.

Answer 1

Position of Point -> 'A'

Position of Helicopter -> 'B'

Position of Level Ground -> 'GD'

Position of Reflection -> 'E'

From the figure :

( tan 60° ) = AF / FE = ( 200 + h ) / x ---> [ ΔAFC ]

( tan 30° ) = BC / AC = ( h / x ) ---> [ ΔBCA ]

Dividing above two equations :

( tan 60° ) ÷ ( tan 30° ) = ( 200 + h ) / h

=> 3h = ( 200 + h )

=> 2h = 200m => h = 100m

→ Hence, the height of helicopter is : BC + CD = 200m