THE ANGLE OF ELEVATION OF A CLOUD FROM A POINT 60 M ABOVE A LAKE IS 30 DEGREE AND THE ANGLE OF DEPRESSION OF THE REFLECTION OF CLOUD IN THE LAKE IS 60 DEGREE. FIND THE HEIGHT OF THE CLOUD.

Dear student,

let height of cloud is H from ground then height of cloud from point is (H-60) ...

using tan30 = (H-60)/d      .........1                (d is the base of upper triangle formed)

image of cloud after reflection is formed at H depth below the water surface , so for lower triangle

 tan60 = (H + 60)/d          ...........2               (d is the base of lower triangle)

dividing 2 by 1

 H+60/H-60 = 3

 H + 60 = 3H - 180

 2H = 240

 H = 120m