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  • If the angle of elevation of a cloud from a point 10 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, find the height of the cloud from the surface of lake.    <div style="f

If the angle of elevation of a cloud from a point 10 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°, find the height of the cloud from the surface of lake. 

 

 

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\\BC=h\\BC'=h+10\\tan30=\frac{h}{x}\\h=\frac{x}{\sqrt{3}}\\x=h\sqrt{3}\\From\ triangle ABC'\\tan60=\frac{h+10}{x}\\\sqrt{3}=\frac{h+10}{x}\\3h=h+10\\2h=10\\h=5m

Height of the cloud from the surface of the lake=5+10+5=20m

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