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A spherical ballon of radius r while flo...

A spherical ballon of radius r while floating in the sky, makes an angle `alpha` in the eye of viewer. If the angle of elevation of the centre of the ballon in the eye of the viewer be `beta`, show that the altitude of the centre of the ballon from the ground is `r cosec alpha/2 sin beta`.

Text Solution

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Let O be the centre of the balloon of radius which subtends an angle` alpha` at E , the eyes of observer .

EA and EB are the tangents to the balloon .
`therefore angle OEA = angle OEB =alpha//2`
Let the height OL of the balloon be h .
In `Delta` OLE ,
h=OE sinbeta
`= rcosec(alpha//2)sinbeta` ( in triangle OBE)
`=(rsinbeta)/(sin(alpha//2))`
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