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UPSC CDS Math Height and Distances Questions

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On the top of a hemispherical dome of radius r, there stands a flag of height h. From a point on the ground, the elevation of the top of the flag is 30°. After moving a distance d towards the dome, when the flag is just visible, the elevation is 45°. The ratio of h to r is equal to

√2−1
√3+1
2√2
√3+1
2√2
d
(√3+1)(√2−1)
2√2
d

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