Math Analysis

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From a ship off-shore, the angle of elevation of a hill is 1.1°. After the ship moves inland at 4.5 knots for 20 min, the angle of elevation is 1.4°. How high is the hill? (1 knot = 1 nautical mile = 6080 ft per hour)


As I was just about to get the answer, I realized that it was gonna be negative, which is definitely not correct. I apologize that I can't include a picture to clarify the problem a bit. Could someone maybe please explain how to get the answer? Any help is greatly appreciated! :)

  • Math Analysis -

    Ok, let's make a diagram showing the sideview.
    Let A be the origianl position of the ship, let B be the position after 20 minutes, Let P be the top of the hill, and Q be on AB extended so that BQ and PQ form a right angle.
    Summarizing:
    angle Q = 90º, angle QBP = 1.4º, angle BAP = 1.1º
    and AB = 4.5(20/60) = 1.5 nautical miles

    By exterior angles, angle ABP = 178.6º
    and angle APQ = .3 º

    by sine law: BP/sin1.1 = 1.5/sin).3
    5.49969 nautical miles or 33438 feet

    now in right-angled triangle BQP
    PQ/33438 = sin 1.4
    PQ = 816.966 feet

    the hill is appr. 817 feet high

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