Question

A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its center is φ, find the height of the center of the balloon. rsin cos / 2

Answer 1

Answer:

Step-by-step explanation:

let's the hight of centre of the balloon above the ground be = h meter..

since the balloon subtends an angle at = theeta

now suppose that

Now

 angle(EAD) = alpha

in △ACE = △ACD

AE = AD... [ lengths of tangents drawn from an external point to the circle are equal ]

 AC = AC.... [ common ]

angle(CEA) = angle(CDA) = 90 ...[ radius is perpendicular to tangent at point of contact ]

△ACE. ≈ △ACD

 angle(EAC) = angle(DAC)...[C.P.C.T ]

 angle(EAC) = angle(DAC) = alpha/2

in right △ACD

sin(altha/2) = CD/AC

AC = r/sin(alpha/2) _____eq(1)

Now in right △ABC

sin(pai) = CB/AC

=> CB = AC×sin(pai)