Question

A drone is flying at a height of h metres. At an instant it observes the angle of elevation of the top of an industrial turbine as 60° and the angle of depression of the foot of the turbine as 30°. If the height of the turbine is 200 metres, find the value of h and the distance of the drone from the turbine. (Use `sqrt(3)` = 1.73)

Answer 1

In ΔABC,

tan 30° = `(AB)/(BC)`

tan 30° = `h/x`

`1/sqrt(3) = h/x`

⇒ x = `hsqrt(3)`   ...(1)

In ΔAED,

tan 60° = `(200 - h)/x`

`sqrt(3) = (200 - h)/x`

`xsqrt(3) = 200 - h`

Substitute the value of x from (1).

`hsqrt(3) xx sqrt(3) = 200 - h`

3h + h = 200

h = `200/4`

h = 50 m

From the equation (1)

x = `50sqrt(3)`

= 50 × 1.73

= 86.50 m

The height of the drone is 50 m, and the distance of the drone from the turbine is 86.50 m.