document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #725785 by addingup(3677) $\"\"$ $\"About$

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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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\n" ); document.write( "I'll call the distance between the tips x
\n" ); document.write( "Law of cosines: x^2 = a^2 + b^2 - 2*a*b*cos60
\n" ); document.write( "x^2 = 4^2 + 6^2 - 2*4*6*cos60
\n" ); document.write( "x^2 = 16 + 36 - 48*0.5
\n" ); document.write( "x^2 = 52 - 24
\n" ); document.write( "x^2 = 28
\n" ); document.write( "x ≈ 5.29 cm. This is the distance between the tips of the hands at 2 o'clock. \n" ); document.write( "

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