JEE Main 2017MathematicsHeights and DistancesEasyMCQ

JEE Main 2017 — Heights and Distances Question with Solution

JEE Main 2017 (02 Apr)

Question

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that  AP=2AB. If ∠BPC=β, then tanβ is equal to:

Choose an option

Show full solutionCorrect option: C
Correct answer
C29

Step-by-step explanation

Let ∠APC=α
Given, AB=2AC=2BC

Also AP=2AB⇒AP=4AC=4BC

⇒tanα=ACAP=AC4AC=14

⇒tanα+β=ABAP=AB2AB=12

Let, tanβ=x

tanα+tanβ1-tanα ⋅tanβ=12

⇒ 14+x1-x4=12

⇒ 1+4x4-x=12

⇒  2+8x-4+x=0

⇒  9x-2=0

⇒  x=29

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About this question

This is a previous-year question from JEE Main 2017, 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.