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pre calc

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the hour hand of a clock is 5 inches long and the minute hand is 6 inches long. Determine the distance between the tips of the hand at 11:40 p.m.
please help i don't understand how to do this.
if you work it out this will help alot

  • pre calc -

    The hard part is finding the angle between the two hands.
    Each hour represents 30°
    so 11:40 = 11 2/3 hrs of rotation
    the hour had is at the 350° position and the minute hand is at the 240° position,
    so the angle between the two hands is 350-240 = 110°
    now use the cosine law:
    x^2= 5^2 + 6^2 - 2(5)(6)cos 110°
    = 61 - 60cos110
    = 81.5212
    x = √81.5212 = 9.03 inches.

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