LIC AAO Prelims practice question
Two boats are approaching a lighthouse of height 100 m from opposite sides, both in line with its base. At a certain moment, the angles of depression of the two boats from the top of the lighthouse are 60° and 30°. Find the distance between the two boats at that moment.
From a LIC AAO Prelims Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) 230.9 m
Let O be the foot of the lighthouse. Since the boats are on opposite sides, the first boat is at distance h·cot(60°) = 100 × 0.6 = 57.7 m from O, and the second boat is at distance h·cot(30°) = 100 × 1.7 = 173.2 m from O on the other side. The distance between the boats = 57.7 m + 173.2 m = 230.9 m.
हिंदी में प्रश्न
100 मी ऊँचे एक लाइटहाउस के आधार की सीध में, विपरीत दिशाओं से दो नावें लाइटहाउस की ओर आ रही हैं। एक निश्चित क्षण पर, लाइटहाउस की चोटी से दोनों नावों के अवनमन कोण क्रमशः 60° और 30° हैं। उस क्षण दोनों नावों के बीच की दूरी ज्ञात कीजिए।
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सही उत्तर: (A) 230.9 m
मान लीजिए लाइटहाउस का आधार O है। चूँकि नावें विपरीत दिशाओं में हैं, पहली नाव O से h·cot(60°) = 100 × 0.6 = 57.7 m दूरी पर है, और दूसरी नाव दूसरी ओर O से h·cot(30°) = 100 × 1.7 = 173.2 m दूरी पर है। दोनों नावों के बीच की दूरी = 57.7 m + 173.2 m = 230.9 m।
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