JEE Main 2015MathematicsHeights and DistancesEasyMCQ

JEE Main 2015 — Heights and Distances Question with Solution

JEE Main 2015 (04 Apr)

Question

If the angles of elevation of the top of a tower from three collinear points A, B and C on a line leading to the foot of the tower are 30°, 45° and 60° respectively, then the ratio AB:BC, is

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Show full solutionCorrect option: B
Correct answer
B 3  : 1

Step-by-step explanation

Let, the height of the tower=h

Let, AB=x, BC=y, CD=z

In ∆ADE, tan⁡30o= hx+y+z

⇒x+y+z=3h  ...i

In ∆BDE, tan45°=hy+z

⇒y+z=h  ...ii

In ∆CDE, tan60°=hz

⇒z=h3  ...iii

From ii & iii, 

y=h1- 13  ...iv

From i & ii, 

x=3-1h  ...v

∴ ABBC=xy= 3-1hh3-13= 31

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About this question

This is a previous-year question from JEE Main 2015, 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.