Question

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30 degree. The angle of depression of the reflection of the cloud in the lake, at A is 60 degree. Find the distance of the cloud from A.

Answer 1

see diagram, here it is given that AB is the height of point A from water lake. let cloud is located at E and its reflection from water is located at F.

if we assume distance of cloud from point A.
e.g., DE = h and CF = h - 20

now, from ∆ADE,

tan30° = DE/AD

1/√3 = h/AD

AD = √3h ..............(1)

from triangle ∆ADF,

tan60° = DF/AD

√3 = (FC + CD)/√3h

√3 × √3h = (h + 20 + 20)

3h = h + 40

h = 20m.

hence, distance of cloud from A = 20m

Answer 2

Answer:

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