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Height and Distance
Height and Distance
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Question

If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30 o and the angle of depression of reflection of the cloud in the lake from P be 60 o , then the height of the cloud (in meters) from the surface of the lake is :

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Solution

tan 30 o = xy⇒y=3x    ....(i){x \over y} \Rightarrow y = \sqrt 3 x\,\,\,\,....(i) tan 60 o = 25+x+25y{{25 + x + 25} \over y} ⇒  3y=50+x \Rightarrow \,\,\sqrt 3 y = 50 + x ⇒\Rightarrow 3x=50+x3x = 50 + x ⇒\Rightarrow x = 25 m ∴\therefore Height of cloud from surface = 25 + 25 = 50m

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