If a man standing on a platform 3 m 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.

Question

Philoid · Accepted Answer

False

Let P be the point where the man is standing and C be the point where the cloud is. MO = 3 m, the platform’s height from the surface of the lake.

The angles, θ₁= the angle of elevation of the cloud and θ₂ = the angle of depression of the cloud.

The height of reflection of cloud is h+3 because height of lake is also added to the platform’s height.

So, the angle of depression is different in lake to the angle of elevation of cloud above the surface of the lake.

In

Or …eq. 1

In

Or

Or …eq. 2

From eq. 1 and eq. 2,

⇒ θ₂ ≠ θ₁

(∵, is an extra factor, that is why tan θ₁ and tan θ₂ cannot be equal and so θ₁ and θ₂ cannot be equal)

∴ This proves that angle of elevation is not equal to the angle of depression of the sun.