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
Answers
Answered by
1
Answer:
a I guess if not then I am sorry
Answered by
1
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.
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