Question

If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
A. 200 m
B. 500 m
C. 30 m
D. 400 m

Answer 1

Answer:

a I guess if not then I am sorry

Answer 2

D. 400 m

Step-by-step explanation:

Please refer to the attached picture for the diagram.

Let AB be the lake surface and P be the point of observation such that AP = 200 m. Let C be the position of cloud and C′ be its reflection in the lake. Then CB = C′B Let CM = x Then CB = CM + MB = x + 200

In ∆CPM, we get tab 30 = CM / PM

  1/√3 = x/AB

So AB = x√3 -----------(1)

In ∆PMC′, we get tan 60 = C′M / PM

 √3 = x+400 / AB

 AB = x+400/√3-----------(2)

From 1 and 2, we get:

 x√3 = x+400/√3

 3x = x +400

 2x = 400

Therefore x = 200m

Height of the cloud = x + 200 = 400m.

Option D is the answer.