If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Write ‘True’ or ‘False’ and justify your answer
Solution:
Given, a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake.
We have to determine if the angle of elevation of the cloud is equal to the angle of depression of its reflection.
Let M be the position where a man is standing on a platform.
C is the cloud
MO is the height of the platform from the surface of the lake.
MO = 3 m
Let θ₁ be the angle of elevation
Let θ₂ be the angle of depression
Height of reflection of the cloud = (h + 3) m
In triangle MPC,
tan θ₁ = CM/PM
tan θ₁ = h/PM
PM = h/tan θ₁ ------------------- (1)
In triangle MPC’,
tan θ₂ = C’M/PM
tan θ₂ = (h + 3)/PM
PM = (h + 3)/tan θ₂ ----------------- (2)
From (1) and (2),
h/tanθ₁ = (h + 3)/tanθ₂
h(tanθ₂) = (h + 3) tanθ₁
So, tanθ₁ = h/(h + 3) tanθ₂
It is clear that θ₁ ≠ θ₂
Therefore, the angle of elevation is not equal to the angle of depression.
✦ Try This: From the top of a cliff 200ft. high, the angle of depression of the top and bottom of the tower are observed to be 30 and 60 respectively. The height of the tower is
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.2 Problem 8
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection” is false
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