Question

A spherical balloon of radius r subtends an angle theta at the eye of
an observer. If the angle of elevation of its centre is phi , find the height of the centre of
the balloon.​

Answer 1

Step-by-step explanation:

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)