Verified Solution • 2025–26 Session moderate

QJEEM20Ma6843: JEE Main 2020 Mathematics - Class 12 JEEM20Ma6843 Solution: The angle of elevation of the summit of a mountain from a point …

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is :

Multiple Choice Options

  • A 13−1{1 \over {\sqrt 3 - 1}}
  • B 3+13−1{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}
  • C 13+1{1 \over {\sqrt 3 + 1}}
  • D 3−13+1{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 6th September Evening Slot Mathematics - Height and Distance Question 20 English Explanation

In Δ\Delta CDF

sin 30o = z1{z \over 1}

⇒\Rightarrow z = 12{1 \over 2} km

cos 30o = Y1{Y \over 1}

⇒\Rightarrow Y = 32{{\sqrt 3 } \over 2} km

Now in Δ\Delta ABC,

tan 45o = hX+Y{h \over {X + Y}}

⇒\Rightarrow h = X + Y

⇒\Rightarrow X = h - 32{{\sqrt 3 } \over 2}

Now in Δ\Delta BDE

tan 60o = h−zX{{h - z} \over X}

⇒\Rightarrow 3{\sqrt 3 } X = h - 12{1 \over 2}

⇒\Rightarrow 3(h−32)\sqrt 3 \left( {h - {{\sqrt 3 } \over 2}} \right) = h - 12{1 \over 2}

⇒\Rightarrow h = 13−1{1 \over {\sqrt 3 - 1}} km

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