Question

    A man standing in a point C of a ground. He observes a flying an aero-plane in the east at an angle of elevation of 30° and after 30 seconds, he observes the same aero-plane in the west at an angle of elevation of 60°. If the aero-plane flies all along in a straight line at a height of 480√3 m, then its speed in km/h is:

    A 247.8 Correct Answer Incorrect Answer
    B 257.5 Correct Answer Incorrect Answer
    C 230.4 Correct Answer Incorrect Answer
    D 249.8 Correct Answer Incorrect Answer

    Solution

    From the following figure, AB = ED = 480√3 AE = BD In Δ ABC, tan 30 = AB/BC 1/√3 = 480 √3/BC BC = 480 × 3 = 1440 In Δ EDC, tan 60 = ED/DC √3 = 480 √3/DC

    DC = 480
    BD = BC + DC = 1440 + 480 = 1920 Aeroplane cover 1920 m distance in 30 seconds. ∴ Speed of aeroplane = 1920/30 × 18/5 = 230.4 km/hr

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