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A spherical balloon of radius r subtends...

A spherical balloon of radius r subtends an angle `alpha` at the eye of anb observer. If the angle of elevation of the cerntre of the balloon be `beta`, then prove that the height of the balloon is
r `cosec (alpha)/(2) sin beta.`

Text Solution

Verified by Experts

[Hint : `angleQPC = alpha`
`therefore " " angleQPB = angle BPC = (alpha)/(2)`
`anglePQB = 90^(@)`
`sin(alpha)/(2) = (QB)/(PB)=(r)/(l)`
`rArr " " l sin (alpha)/(2) = r`
`rArr l = (r)/(sinfrac(alpha)(2))=r cosec (alpha)/(2)`..............(1)
In `DeltaPOB, sinbeta = (OB)/(PB) = (h)/(l)` ltbtgt `rArr h = l sin beta`
`rArr h=r cosec (alpha)/(2) sin beta`.(Proved)]
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