Question

A round ball of radius r substend an angle α at the eye of the observer whose angle of elevation of centre is β.Prove that the height of the centre of the baloon is

Answer 1

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Answer 2

Answer:

1. h=r sinβ csc α/2

Step-by-step explanation:

• let op=r
• ob=h
• ao=y
• centre of the circle lies on the angle bisector of angle PAQ
• Which implies angle OAP =alpha/2
• Angle OAB= beeta
• we know that radius is perpendicular to tangent .
• so in triangle APO
• cosec alpha/2=y/a
• y=r cosec alpha/2..............(1)
• in triangle ABO
• sin beeta =h/y
• y=h/sin beeta................(2)
• (1) &(2) implies
• h/sin beeta =r cosec alpha/2
• h=r sinβ csc α/2
• hence proved