Verified Solution • 2025–26 Session moderate

QJEEM19Ma8a2f: JEE Main 2019 Mathematics - Class 12 JEEM19Ma8a2f Solution: Consider a triangular plot ABC with sides AB = 7m, BC = 5m and…

Consider a triangular plot ABC with sides AB = 7m, BC = 5m and CA = 6m. A vertical lamp-post at the mid point D of AC subtends an angle 30o at B. The height (in m) of the lamp-post is -

Multiple Choice Options

  • A 2212\sqrt {21}
  • B 3221{3 \over 2}\sqrt {21}
  • C 737\sqrt {3}
  • D 2321{2 \over 3}\sqrt {21}

Step-by-Step Verified Solution

JEE Main 2019 (Online) 10th January Morning Slot Mathematics - Height and Distance Question 29 English Explanation
BD = hcot30o = h 3\sqrt 3

So, 72 + 52 = 2(h 3\sqrt 3 )2 + 32)

⇒\Rightarrow   37 = 3h2 + 9

⇒\Rightarrow   3h2 = 28

⇒\Rightarrow   h = 283=2321\sqrt {{{28} \over 3}} = {2 \over 3}\sqrt {21}

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