document.write( "Question 412206: theta is a central angle in a circle of radius r = 5 mm. Find the length of arc s cut off by theta; = 330°. (Round the answer to two decimal places.) How do you work this problem? \n" ); document.write( "

Algebra.Com's Answer #289666 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Central angles, their arcs and the areas of the sectors formed are all proportional:
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document.write( "     central angle           arc length           area of sector\r\n" );
document.write( "  ------------------    =   -------------   =   ------------------\r\n" );
document.write( "  2pi or 360 degrees        Circumference       area of the circle\r\n" );
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\n" ); document.write( "For your problem, which references central angles and arc length we will use the first two fractions:
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document.write( "     central angle           arc length\r\n" );
document.write( "  ------------------    =   -------------\r\n" );
document.write( "  2pi or 360 degrees        Circumference\r\n" );
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\n" ); document.write( "Since your central angle is expressed in degrees we will use 360 in the denominator of the first fraction:
\n" ); document.write( " $\"330%2F360+=+x%2F%282%2Api%2A5%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"11%2F12+=+x%2F10pi\"$
\n" ); document.write( "Cross multiplying we get:
\n" ); document.write( " $\"110pi+=+12x\"$
\n" ); document.write( "Dividing by 12 we get:
\n" ); document.write( " $\"110pi%2F12+=+x\"$
\n" ); document.write( "All that's left is to replace $\"pi\"$ with a decimal (3.14158....) and simplify the fraction. I'll leave that up to you. \n" ); document.write( "

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