Question : The angle of elevation of a cloud from a point 60 metres above a lake is 30Â - Maths -

Question

Question :
The angle of elevation of a cloud
from a point 60 metres above a lake is 30
Â° and the angle of
depression of the reflection of the cloud in the lake is 60
Â° Find the height of the
cloud

Koka Sri Lakshmi Divya Sai · Accepted Answer

$Given AP=60m \Rightarrow AP=BQ=60m ∠ Q P C = 30^{0} and ∠ Q P D = 60^{0} Let h be the height of the cloud CQ= (h - 60) m DQ= (h + 60) m From Δ CQP we have \frac{PQ}{CQ} = \cot 30^{0} \Rightarrow \frac{PQ}{(h - 60)} = \sqrt{3} \Rightarrow PQ= (h - 60) \sqrt{3} - - - - (i) From Δ DQP we have \frac{PQ}{DQ} = \cot 60^{0} \Rightarrow \frac{PQ}{(h + 60)} = \frac{1}{\sqrt{3}} \Rightarrow PQ= \frac{(h + 60)}{\sqrt{3}} - - - (i i) From (i) and (ii) we have (h - 60) \sqrt{3} = \frac{(h + 60)}{\sqrt{3}} \Rightarrow 3 h - 180 = h + 60 \Rightarrow 2 h = 240 \Rightarrow h = 120 ∴ The height of the cloud =120m \Rightarrow$

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Question : The angle of elevation of a cloud from a point 60 metres above a lake is 30 ° and the angle of depression of the reflection of the cloud in the lake is 60 ° . Find the height of the cloud.

Question :

The angle of elevation of a cloud from a point 60 metres above a lake is 30 ° and the angle of depression of the reflection of the cloud in the lake is 60 ° . Find the height of the cloud.