Heights and Distances Practice Test 1

Let O be the centre of the balloon of radius r which subtend an angle α at the eye of an observer at E.
If EA and EB are the tangents to the balloon,
then ∠OEA = ∠OEB =

α

2

In ΔOAE, sin

1

2

α = OA/OE
∴ OE = r cosec

1

2

α
In ΔOEL, height of the centre of the balloon = h = OE sin β = r cosec

1

2

α sin β