Cosine Law

The minute hand of a clock is 12 cm long, and the hour hand is 10cm long. Determine the distance between the tips of the hands at 9:30pm, to the nearest mm.

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asked by Jane
  1. At 12:00 the hands are together
    After h hours, the hour hand has gone h/12 * 360 degrees
    After m minutes, minute hand has gone m/60 * 360 degrees
    9:30 = 9.5 hours
    :30 = 30 minutes
    So, the hour hand has gone 9.5/12*360 = 285° and the minute hand is at 180°

    So, the angle between the hands is 105°

    Finally, the distance d between the tips is

    d^2 = 12^2 + 10^2 - 2*10*12 cos105°

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    posted by Steve

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