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A spherical balloon of radius r subtends an angle α at an observer's eye, and the angle of elevation of its centre is β. How high is the centre of the balloon above the eye?

Competition practiceTrigonometry
  • Ar sin β cosec (α/2)
  • Br cos β cosec (α/2)
  • Cr sin β sec (α/2)
  • Dr sin (α/2) cosec β

Step-by-Step Solution

The sight lines are tangents, so the distance from the eye to the centre is r/sin(α/2) = r cosec(α/2). The centre's height is that distance × sin β = r sin β cosec(α/2).
Answer: A) r sin β cosec (α/2)

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