A spherical balloon of radius r subtends an angle a at the eye of the observer the centre subtends an angle b at the eye. find h
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Let the height of centre of the balloon above the ground be h m.
Since the balloon subtends an angle θ at the observes eye,
∴ ∠EAD = θ
In ∆ ACE and ∆ ACD,
AE = AD (lengths of tangents drawn from an external point to the circle are equal)
AC = AC (common)
∠CEA = ∠CDA = 90° (Radius is perpendicular to tangent at point of contact)
∴ ∆ ACE ≅ ∆ ACD
⇒ ∠EAC = ∠DAC (C.P.C.T)
Since the balloon subtends an angle θ at the observes eye,
∴ ∠EAD = θ
In ∆ ACE and ∆ ACD,
AE = AD (lengths of tangents drawn from an external point to the circle are equal)
AC = AC (common)
∠CEA = ∠CDA = 90° (Radius is perpendicular to tangent at point of contact)
∴ ∆ ACE ≅ ∆ ACD
⇒ ∠EAC = ∠DAC (C.P.C.T)
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