document.write( "Question 1207171: What is the distance between the tips of the minute hand and the hour hand of a clock at 1:35pm where the length of the minute hand is 14cm and the length of the hour hand is 9cm \n" ); document.write( "

Algebra.Com's Answer #844890 by ikleyn(52792) $\"\"$ $\"About$

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\n" ); document.write( "What is the distance between the tips of the minute hand and the hour hand
\n" ); document.write( "of a clock at 1:35pm where the length of the minute hand is 14cm
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document.write( "At 1:35 pm, the angle between the minute hand and vertical direction up is  \r\n" );
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document.write( "     =  =   radians\r\n" );
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document.write( "(since the minute hand makes a full rotation in 60 minutes).\r\n" );
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document.write( "The angle between the hour hand and vertical direction up is\r\n" );
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document.write( "      +  =  +  = .\r\n" );
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document.write( "(since the hour hand makes a full rotation in 12 hours = 12*60 minutes).\r\n" );
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document.write( "The difference between these angles is\r\n" );
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document.write( "     -  =  -  = .\r\n" );
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document.write( "Thus the angle between the two hands at 1:35 pm is    radians.\r\n" );
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document.write( "It is more than the right angle  = , but less than the straight angle of  = .\r\n" );
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document.write( "Now, we have an obtuse triangle with the sides of 14 cm and 9 cm and the angle of   radians between them.\r\n" );
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document.write( "To find the distance between the tips of the hands, apply the cosine law equation\r\n" );
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document.write( "    d =  = 22.745 cm.\r\n" );
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document.write( "ANSWER.  The distance between the tips is about  22.745 cm.\r\n" );
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