Question

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

Answer 1

Step-by-step explanation:

The angle of elevation of a cloud from a point 60m above a lake is 30° and the angle

of depression of the reflection of the cloud in the lake is 60°. Find the height of the

cloud from the surface of the lake.

Answer 2

Answer:

120 m

Step-by-step explanation:

Given :-

Distance of point from the ground = 60 m

Angle of elevation θ1 = 30°

Angle of depression θ2 = 60°

Find :-

Height of the  cloud from the surface of the lake.

Now,

From triangle ABF,

θ1 = 30°

AB = h

BF = x

Tan θ1 = Opp/Adj

Tan 30° = AB/BF

1 /root 3 = h/x

x = h root 3 -------> 1.

From triangle DBF,

Tan θ2 = Opp/Adj

Tan 60° = h + 60 + 60 / x

root 3 = h + 120 / x

x root 3 = h + 120

h root 3 ( root 3 ) = h + 120

3 h = h +120

2 h = 120

h = 60 m

Therefore,  height of the  cloud from the surface of the lake = h m + 60 m

                                                                                                   = 60 m + 60 m

                                                                                                   = 120 m