Verified Solution • 2025–26 Session moderate

QJEEM20Ma16a8: JEE Main 2020 Mathematics - Class 12 JEEM20Ma16a8 Solution: The angle of elevation of a cloud C from a point P, 200 m above …

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 :

Multiple Choice Options

  • A 2003200\sqrt 3
  • B 400
  • C 100
  • D 4003400\sqrt 3

Step-by-Step Verified Solution

JEE Main 2020 (Online) 4th September Evening Slot Mathematics - Height and Distance Question 23 English Explanation
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 30o = x3PC{{{x \over {\sqrt 3 }}} \over {PC}}

⇒\Rightarrow PC=2x3PC = {{2x} \over {\sqrt 3 }}

⇒PC=400\Rightarrow PC = 400

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring