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 .
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.
OP= r cosec…(i)
OL = r sinф cosec (from (i))
Thus, the height of the centre of the balloon is r sinф cosec.
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