SOLUTION: The lengths of the hour and minute hands of a clock are 4 cm and 6 cm respectively. What is the distance, in cm, between the tips of the hands at 2 o'clock?
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Question 1110754: The lengths of the hour and minute hands of a clock are 4 cm and 6 cm respectively. What is the distance, in cm, between the tips of the hands at 2 o'clock? Found 2 solutions by ikleyn, addingup:Answer by ikleyn(52754) (Show Source):
The angle between the hands at that time is = 60 degrees.
Now apply the cosine law:
c^2 = 6^2 + 4^2 - 2*6*4*cos(60) = 36 + 16 - 2*6*4*(1/2) = 28.
Hence, the distance under the question is = 5.29 cm (approximately).
You can put this solution on YOUR website! In order to calculate the distance between the tips of the hands, first you have to find the angle between both hands. I get 60 degrees. So we have an equilateral triangle with angles 60-60-60.
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I'll call the distance between the tips x
Law of cosines: x^2 = a^2 + b^2 - 2*a*b*cos60
x^2 = 4^2 + 6^2 - 2*4*6*cos60
x^2 = 16 + 36 - 48*0.5
x^2 = 52 - 24
x^2 = 28
x ≈ 5.29 cm. This is the distance between the tips of the hands at 2 o'clock.
