document.write( "Question 378973: the central angle theta of a circle with radius 9 inches intercepts an arc 20 inches, find theta \n" ); document.write( "

Algebra.Com's Answer #269272 by jsmallt9(3758) $\"\"$ $\"About$

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This problem can be solved with a simple proportion:
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document.write( "          Angles              Arcs         \r\n" );
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document.write( "Part:     central angle          intercepted arc\r\n" );
document.write( "          -----------------  =  -------------------\r\n" );
document.write( "Total:    full circle (360)      full circumference\r\n" );
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\n" ); document.write( "(Since Algebra.com's software doesn't \"do\" theta, I am going to use q in place of theta. So replace any q's below with theta.)
\n" ); document.write( "Your proportion is, therefore:
\n" ); document.write( " $\"q%2F360+=+20%2F%282%2A9%2Api%29\"$ (Since Circumference = 2*r*pi.)
\n" ); document.write( "This simplifies as follows:
\n" ); document.write( " $\"q%2F360+=+10%2F%289%2Api%29\"$
\n" ); document.write( "To solve for q we start by cross-multiplying:
\n" ); document.write( " $\"q%2A9pi+=+360%2A10\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"q%2A9pi+=+3600\"$
\n" ); document.write( "Next we divide by $\"9pi\"$
\n" ); document.write( " $\"q+=+3600%2F%289pi%29\"$
\n" ); document.write( "The fraction reduces:
\n" ); document.write( " $\"q+=+400%2Fpi\"$
\n" ); document.write( "So q (or theta) is $\"400%2Fpi\"$ degrees. \n" ); document.write( "

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