A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, find the height of the centre of the balloon
Solution:
From the figure, O is the centre of balloon, whose radius OP = r and ∠PAQ = θ.
∠OAB = φ
Consider the height of the centre of the balloon be h
So OB = h.
In ∆OAP,
sin θ/2 = r/d, where OA = d ….. (1)
In ∆OAB,
sin φ = h/d ….. (2)
From equations (1) and (2)
sin φ/ sin θ/2 = h/d/ r/d = h/r
or h = r sin φ cosec θ/2
Therefore, the height of the centre of the balloon is h = r sin φ cosec θ/2.
✦ Try This: A spherical balloon of radius r subtends an angle α at the eye of an observer, when the angular elevation of its centre is β.The height of the centre of the balloon is
- r sin α/2 cosec β
- r cosec α sin β/2
- r cosec α/2 sin β
- r sin α cosec β/2
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.4 Sample Problem 1
A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, find the height of the centre of the balloon
Summary:
A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is φ, the height of the centre of the balloon is h = r sin φ cosec θ/2
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