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Two ships are on the same side of a lighthouse. The angles of depression from the top of the lighthouse, 100 m high, are 30 degrees and 45 degrees. The distance between the ships is
A100 (square root of 3 + 1) m
B100 m
C100 (square root of 3) m
D100 (square root of 3 - 1) m
Answer & Solution
Correct answer: D. 100 (square root of 3 - 1) m
1. From lighthouse, far ship distance = 100/tan(30) = 100 (square root of 3).
2. Near ship distance = 100/tan(45) = 100.
3. Difference = 100 (square root of 3) minus 100 = 100 (square root of 3 minus 1) m.
_Source: NCERT Class 10 Mathematics, Ch 9 "Some Applications of Trigonometry", §9.2_
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