JEE Main 2019MathematicsHeights and DistancesHardMCQ

JEE Main 2019 — Heights and Distances Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

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-132 and cosec-122 respectively, then the height of the tower (in metres) is

Choose an option

Show full solutionCorrect option: B
Correct answer
B20

Step-by-step explanation

Let AD=y & DE=h (Tower)

∴ y2=1002-x2

Now cotθ=32

⇒tanθ=132=hy

⇒y=32h

⇒y2=1002-x2=18h2  …1

⇒tan∅=17=hx

⇒x=h7    …2

Form 1 & 2 1002-7h2=18h2

⇒ 25h2=1002⇒h=20

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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.