Question

The angle of elevation of a cloud from a point hundred metre above the surface of a lake is 30 degree and the angle of depression of the reflection of the cloud in the lake is 60 degree then find the height of the cloud from the lake surface?

Answer 1

$Solution:$

Let height of the cloud from the leaves surface be h metres.

Also, let CQ = x metres.

From right ∆AQC, we get

$\frac{x}{AQ} = tan30°$

$= > \frac{x}{AQ} = \frac{1}{ \sqrt{3} }$

$= > AQ = x \sqrt{3} m$

From right ∆AQC', we get

$= > \frac{C'Q}{AQ} = tan60$

$= > \frac{C'P + PQ}{AQ} = { \sqrt{3} }$

$= > \frac{100 + x + 100}{x \sqrt{3} } = { \sqrt{3}}$

$= > 200 + x = 3x$

$= > 2x = 200$

$= > x = \frac{200}{2}$

$= > x = 100$

$Therefore, x = 100m.$

So,

CP = CQ + PQ

CP = (100 + 100)m

CP = 200 m.

Thus, cloud is at a height of 200 metre from the lake surface.

$[Ans: 200m]$

Answer 2

Answer:

Let A be the cloud and D be its shadow.

BC = 60 m  

Height of cloud = h m .

Total height of cloud = h + 60 m  

In  Δ ABE

h / x = tan 30

x = h √ 3

In Δ BDE

h + 60 + 60 / x  = tan 60

h + 120 = x √ 3

2 h = 120

h = 60 m .

Therefore , height of cloud from surface of water = ( 60 + 60 ) = 120 m .