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  • The angle of elevation of a cloud C from a point P, 200 m above a still lake is . If the angle of depression of the images of C in the lake from the poin

The angle of elevation of a cloud C from a point P, 200 m above a still lake is 30^{\circ}. If the angle of depression of the images of C in the lake from the point P is 60^{\circ}, then PC (in m) is equal to:
Option: 1 100
Option: 2 200 \sqrt{3}
Option: 3 400
Option: 4 400\sqrt{3}

Answers (1)

best_answer

Let PA = x

For triangle APC

\\\mathrm{AC}=\frac{\mathrm{PA}}{\sqrt{3}}=\frac{\mathrm{x}}{\sqrt{3}} \\ \mathrm{AC}^{1}=\mathrm{AB}+\mathrm{BC}^{1} \\ \mathrm{AC}^{1}=400+\frac{\mathrm{x}}{\sqrt{3}}

\\\text { From } \Delta \mathrm{C}^{1} \mathrm{PA}: \mathrm{AC}^{1}=\sqrt{3} \mathrm{PA} \\ \Rightarrow\left(400+\frac{\mathrm{x}}{\sqrt{3}}\right)=\sqrt{3} \mathrm{x} \Rightarrow \mathrm{x}=(200)(\sqrt{3}) \\ \text { from } \Delta \mathrm{APC}: \mathrm{PC}=\frac{2 \mathrm{x}}{\sqrt{3}} \Rightarrow \mathrm{PC}=400

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himanshu.meshram

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