Spherical Balloon Subtending an Angle

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Some Applications of Trigonometry

Spherical Balloon Subtending an Angle

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 5

The problem

A spherical balloon of radius rr subtends an angle α\alpha at the eye of an observer, while the angle of elevation of its center is β.\beta. Prove that the height of the center of the balloon is rsin⁡βcsc⁡(α2).r\sin\beta\csc\left(\dfrac{\alpha}{2}\right).

Step 1 · Your move

Tangents PAPA and PBPB from observer PP touch the balloon at AA and BB, subtending total angle α\alpha. What is the angle ∠APO\angle APO made by the line of centers OPOP?

amber: elevation βteal: angle α/2hPLOAB
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