A sphere with centre O sits atop a pole as shown in the figure. An observer on the ground is at a distance 50 ~m from the foot of the pole. She notes that the angles of elevation from the observer to points P and Q on the sphere are 30^ and

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A sphere with centre O sits atop a pole as shown in the figure. An observer on the ground is at a distance 50 ~m from the foot of the pole. She notes that the angles of elevation from the observer to points P and Q on the sphere are 30^ and 60^ , respectively. Then, the radius of the sphere in meters is -

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Correct answer: C. 50 (1- 1 3 )

DE = BC = r 30^ = h 50 ~h = 50 3 60^ = h + r 50- r 3 (50- r )= h + r 3 (50- r )= 50 3 + r 3(50- r )=50+ 3 r 100=(3+ 3 ) r r= 100 3+ 3 r= 100(3- 3 ) 6 =50 (1- 1 3 )

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