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    Question

    A Navy captain going away from a lighthouse at the speed

    of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60o to 45o. What is the height (in metres) of the lighthouse?
    A 240√3 Correct Answer Incorrect Answer
    B 480[(√3) – 1] Correct Answer Incorrect Answer
    C 360√3 Correct Answer Incorrect Answer
    D 280√2 Correct Answer Incorrect Answer

    Solution

    Let height is H tan 600 = H / BD = BD = H / tan600 [BD = H / √3 tan 450 = AB / BC = AB = BC, BC = H 4(√3 – 1) m/s speed Time = 1 minute 60 Second Distance = Speed × Time = 4√3 – 1) × 60 = 240√3 – 240 CD = 240√3 – 60 CD = H – H/√3 = 240√3 – 240 H(√3 – 1) = 240√3(√3 – 1) H = 240√3 m

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