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Height and Distance
Height and Distance
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Question

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30°. If the angle of depression of the image of C in the lake from the point P is 60°,then PC (in m) is equal to :

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Solution

Let PA = x For Δ\Delta APC AC=PA3=x3AC = {{PA} \over {\sqrt 3 }} = {x \over {\sqrt 3 }} AC1=AB+BC1A{C^1} = AB + B{C^1} AC1=200+x3A{C^1} = 200 + {x \over {\sqrt 3 }} From ΔC1PA,\Delta {C^1}PA, AC1=3PAA{C^1} = \sqrt 3 PA ⇒(200+x3)=3x\Rightarrow \left( {200 + {x \over {\sqrt 3 }}} \right) = \sqrt 3 x ⇒x=(200)(3)\Rightarrow x = (200)(\sqrt 3 ) From ΔAPC,\Delta APC, sin 30 o = x3PC{{{x \over {\sqrt 3 }}} \over {PC}} ⇒\Rightarrow PC=2x3PC = {{2x} \over {\sqrt 3 }} ⇒PC=400\Rightarrow PC = 400

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