Question

A round ballon of radias r makes an angle alpha at the eye of the observer while the angle of elevation of its Centre is beta prove that the height of the centre of the balloon is rSinβcosec α/2

Answer 1

Step-by-step explanation:

See the given figure,

Let the radius of the balloon be 'r' and AO be the height of the centre of the balloon from the ground. Let P be the observer.

In △OPB ,

Cosec α/2 = OP/r

=> OP = (r cosec α/2) ......(i)

In △OPA ,

Sinβ = OA/OP

Sin β = OA / (rCosec α/2) (from i)

OA = rSinβcosecα/2

Hence,Height of the centro of the balloon is rSinβCosecα/2.

Answer 2

Hey mate

refer to the attachment