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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Heights and Distances

JEE Main 2020 · 4 September · Evening Shift · Mathematics · Heights and Distances

The angle of elevation of a cloud C from a point P, 200m above a...

The angle of elevation of a cloud CC from a point P,200mP, 200m above a still take is 30o{30}^{o}. If the angle of depression of the image of CC in the lake from the point PP is 60o{60}^{o}, then PCPC (in mm) is equal toThe angle of elevation of a cloud C from a point P, 200m above a still take is 30 ^ o . If the angle of depression of

Options

  1. A100100
  2. B2003200\sqrt{3}
  3. C400400
  4. D4003400\sqrt{3}

Correct answer

C. 400400

Step-by-step solution

The angle of elevation of a cloud C from a point P, 200m above a still take is 30 ^ o . If the angle of depression of

tan⁡30°=xy=13⇒y=3xand\tan 30 ° = \dfrac{x}{y} = \dfrac{1}{\sqrt{3}} ⇒ y = \sqrt{3}x\text{and}

tan⁡60°=x+400y\tan 60 ° = \dfrac{x + 400}{y}

So, x+400=3y=3xx + 400 = \sqrt{3}y = 3x

2x=400,x=2002x = 400, x = 200

sin⁡30°=200PC⇒PC=400\sin 30 ° = \dfrac{200}{PC} ⇒ PC = 400

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