JEE Main 2019MathematicsHeights and DistancesHardMCQ

JEE Main 2019 — Heights and Distances Question with Solution

JEE Main 2019 (10 Jan Shift 1)

Question

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

Choose an option

Show full solutionCorrect option: B
Correct answer
B2321

Step-by-step explanation

 

The length of the median BD is given by 

BD=122BC2+BA2-AC2

⇒BD=12 225+49-36

⇒BD=12112

⇒BD=472=27 m.

Now, let DT be the tower of height h m and it subtends ∠TBD=30° at the vertex B.

Then, in ∆TDB we have tan∠TBD=TDBD

⇒tan30°=h27

⇒13=h27

⇒h=273

⇒h=2321 m.

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About this question

This is a previous-year question from JEE Main 2019, covering the Heights and Distances chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.