Question

A round ballon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its center is β. prove that the height of the center of the ballon is r sin β cosec alfa/2....​

Answer 1

Answer:

Let O be the centre of the balloon and P be the eye of the observer

And ∠APB be the angle subtended by the balloon

∴∠APB=α

∴∠APO=∠BPO=

2

α

In △OAP,sin

2

α

=

OP

OA

⟹sin

2

α

=

OP

r

⟹OP=r cosec

2

α

−(1)

In △OPC

sinβ=

OP

OL

or OL=OPsinβ

∴OL=r cosec

2

α

sinβ