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A round balloon of radius r subtends an angle at the eye of the

observer while the angle of elevation of its centre is . Prove that the

height of the centre of the balloon is  .

Asked by Topperlearning User 2nd December 2013, 1:34 AM
Answered by Expert


Let O be the centre of the balloon of radius r and P the eye of the observer. Let PA and PB be tangents from P to the balloon. .


Let OL be perpendicular from O to the horizontal.

In ∆OAP,

sin =

OP= r cosec…(i)

In ∆OPL,

sinф =

OL=OP sinф

OL = r sinф cosec (from (i))

Thus, the height of the centre of the balloon is r sinф cosec.

Answered by Expert 2nd December 2013, 3:34 AM
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