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

tan 30 degree = ECAD = 13

tan 30 degree = ECAD = 13 (ED = h)(ED = h) => AD = 3

AD = h 3  ..........(1)

tan 60 degree = FDAD

tan 60 degree = FDAD = 3 under root 3

FD = h + 40 FD=h + 40 = h + 403 under root AD = h + 403  .......(2)

h 3 = h + 403 under root h 3 = h + 403 3 h = h + 403 h = h + 40 2 h = 40 => 

h = 20 m 2 h = 40 => h = 20 m EC = h  

= 20 m EC = h + 20 = 20 + 20 EC = h + 20

= 20 + 20 = 40m