Answer:

120 m

Step-by-step explanation:

Let the lake surface be AB and AP = 60 m. Let the position of the cloud be C and C' be the reflection in lake.

Let CM = x and CB = CM + MB = x + 60.

(i) In ΔCPM

tan 30° = CM/PM

(1/√3) = x/AB

AB = x√3

(ii) In ΔPMC'

tan 60° = C'M/PM

√3 = (x + 120)/AB

AB = (x + 120)/√3

From (i) & (ii), we get

⇒ √3x = (x + 120)/√3

⇒ 3x = x + 120

⇒ 2x = 120

⇒ x = 60

Then:

⇒ x + 60

⇒ 60 + 60

⇒ 120 m.

∴ The height of the cloud = 120 m.

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