Question

The angle of elevation of a bird from a point 40 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the bird.​

Answer 1

Answer:

I am trying to visualise the situation as below. it's not very good but will do the needful.

one thing I would like to add. angle of elevation or angle of depression is always measured with horizontal line.

bird

:

onserver :

|. :. h

|. 40 m :

------------------------------------------------

x :

:

:. h

:

reflection

let the height of the bird from level of Lake be h

depth of the reflection will also be h

let the distance between observer and point on Lake just below bird be x

now

tan 30° = (h-40)/x

1/√3 = (h-40)/x

x = √3(h-40).......(1)

again

tan 60° = (h+40)/x

√3 = (h+40)/x

x= (h+40)/√3.......(2)

from (1) and (2)

√3(h-40) = (h+40)/√3

3(h-40) = h+40

3h - 120 = h + 40

3h - h = 40+120

2h = 160

h = 80 m

Answer 2

Answer:

Step-by-step explanation:

HEY MATE THE ANS IS 80 M . HOPE IT HELPS