Question

The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of cloud in the lake is 60° Find the height of the cloud .​

Answer 1

Hope it will help you........

Answer 2

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.

Hope it helps!