If the angle of elevation of a cloud from a point 200m 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
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Given:
– Observer is 200m above the lake.
– Angle of elevation of cloud = 30°.
– Angle of depression of reflection = 60°.
Using tangent for both angles:
1. tan30° = (h – 200) / d ⇒ d = √3(h – 200).
2. tan60° = (h + 200) / d ⇒ √3 = (h + 200) / d.
Substitute d = √3(h – 200) into the second equation:
√3 = (h + 200) / (√3(h – 200)).
Simplify:
3(h – 200) = h + 200.
Solve for h:
2h = 800 ⇒ h = 400.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
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