Question
Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is :_________?
Answer: Option C
LET AB BE THE LIGHTHOUSE AND C AND D BE THE
POSITIONS OF THE SHIPS. THEN,
AB = 100 M, ∠ACB = 300 AND ∠ADB = 45°.
AB/AC = TAN 30° = 1/√3
AC = AB X √3 = 100√3 M.
AB/AD = TAN 45° = 1 ⇒ AD = AB = 100 M.
CD = (AC + AD) = (100√3 + 100) M
= 100 (√3 +1) M = (100 X 2.73) M = 273 M.
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LET AB BE THE LIGHTHOUSE AND C AND D BE THE
POSITIONS OF THE SHIPS. THEN,
AB = 100 M, ∠ACB = 300 AND ∠ADB = 45°.
AB/AC = TAN 30° = 1/√3
AC = AB X √3 = 100√3 M.
AB/AD = TAN 45° = 1 ⇒ AD = AB = 100 M.
CD = (AC + AD) = (100√3 + 100) M
= 100 (√3 +1) M = (100 X 2.73) M = 273 M.
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