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Question: Answered & Verified by Expert
A balloon moving in a straight line passes vertically above two points A and B on a horizontal plane 300 ft apart. When above A it has an altitude of 45o as seen from B. When above B it has an altitude of 30o as seen from A. The distance of B from the point C where it will touch the plane is
MathematicsHeights and DistancesJEE Main
Options:
  • A 1503+1ft
  • B 150ft
  • C 1503+3ft
  • D 3003+1ft
Solution:
1132 Upvotes Verified Answer
The correct answer is: 1503+1ft


In ABE,
tan30o=h300h=1003ft1
and in ΔABD,
tan45o=H300H=300ft2
Also, HAC=hBC (Similar triangles)
300300+x=1003x [using Eq. 1 and 2 ]
3x=300+x
x=3003-1=1503+1 ft.

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