A round balloon of radius r subtends an angle α at the eye of the
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Let the height of centre of the balloon above the ground be h m.
Given, balloon subtends an θ angle at the observes eye.
∴ ∠ EAD = θ
In ΔACE and ΔACD,
AE = AD (Length of tangents drawn from an external point to the circle are equal)
AC = AC (Common)
CE = CD (Radius of the circle)
∴ ΔACE ΔACD (SSS congruence criterion)
⇒ ∠EAC = ∠DAC (CPCT)
∴ EAC = DAC =
In right ΔACD,
In right ΔACB,
Thus, the height of the centre of the balloon is a .