Heights and Distances Practice Test 1

Question : 36 of 40

Marks: +1, -0

The height of the centre of the round balloon of radius r, which subtend an angle α at the eye of an observer and the elevation of whose centre from the eye is β, is given by:

r sin α sin β
r cosec $1/2$ α sin β
r cosec α sin β
None of these

Validate

Solution:

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

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