Verified Solution • 2025–26 Session moderate

QJEEM19Mae88d: JEE Main 2019 Mathematics - Class 12 JEEM19Mae88d Solution: ABC is a triangular park with AB = AC = 100 metres. A vertical…

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot–1 (3 2\sqrt 2 ) and cosec–1 (2 2\sqrt 2 ) respectively, then the height of the tower (in metres) is :

Multiple Choice Options

  • A 10033{{100} \over {3\sqrt 3 }}
  • B 25
  • C 20
  • D 10 5\sqrt 5

Step-by-Step Verified Solution

JEE Main 2019 (Online) 10th April Morning Slot Mathematics - Height and Distance Question 25 English Explanation Δ\Delta APM

hAM=132{h \over {AM}} = {1 \over {3\sqrt 2 }}

Δ\Delta BPM

hBM=17{h \over {BM}} = {1 \over {\sqrt 7 }}

Δ\Delta ABM

AM2 + MB2 = (100)2

' ⇒\Rightarrow 18h2 + 7h2 = 100 × 100

⇒\Rightarrow h2 = 4 × 100

⇒\Rightarrow h = 20

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