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A man on a hill 200 m high observes that the angles of depression of two consecutive milestones in line directly below are 30 degrees and 45 degrees. The distance between the milestones is
A200 (square root of 3) m
B200 m
C200 ((square root of 3) - 1) m
D100 m
Answer & Solution
Correct answer: C. 200 ((square root of 3) - 1) m
1. Far milestone: distance from foot = 200/tan(30) = 200 (square root of 3).
2. Near milestone: distance from foot = 200/tan(45) = 200.
3. Distance between = 200 (square root of 3) minus 200 = 200 ((square root of 3) minus 1) m.
_Source: NCERT Class 10 Mathematics, Ch 9 "Some Applications of Trigonometry", §9.2_
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