document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062886>Question 1062886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units.\r<BR>\n" );
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document.write( "A: What is the approximate measure of the radius (rounded to the nearest hundredth of a unit)?\r<BR>\n" );
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document.write( "B: What is the approximate area of the circle (rounded to the nearest whole square unit)?\r<BR>\n" );
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document.write( "Select only one answer each for parts A and B.\r<BR>\n" );
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document.write( "	A: 8.09<BR>\n" );
document.write( "	A: 2.63<BR>\n" );
document.write( "	A: 7.69<BR>\n" );
document.write( "	A: 4.25<BR>\n" );
document.write( "	B: 22<BR>\n" );
document.write( "	B: 186<BR>\n" );
document.write( "	B: 206<BR>\n" );
document.write( "	B: 57<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677899 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units.\r<BR>\n" );
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document.write( "A: What is the approximate measure of the radius (rounded to the nearest hundredth of a unit)?\r<BR>\n" );
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document.write( "B: What is the approximate area of the circle (rounded to the nearest whole square unit)?\r<BR>\n" );
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document.write( "Select only one answer each for parts A and B.\r<BR>\n" );
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document.write( "	A: 8.09<BR>\n" );
document.write( "	A: 2.63<BR>\n" );
document.write( "	A: 7.69<BR>\n" );
document.write( "	A: 4.25<BR>\n" );
document.write( "	B: 22<BR>\n" );
document.write( "	B: 186<BR>\n" );
document.write( "	B: 206<BR>\n" );
document.write( "	B: 57<BR>\n" );
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document.write( "Let me show you how to estimate it without using calculator, computer, trigonometric tables and the Internet.<BR>\n" );
document.write( "Using your (or my) BRAIN only !!!\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Since the perimeter is 50 units, the one side length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2F10 ALIGN=MIDDLE  ALT=\"50%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 units.\r\n" );
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document.write( "The central angle leaning one side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F10 ALIGN=MIDDLE  ALT=\"360%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 36 degrees.\r\n" );
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document.write( "One half of this angle is 18 degrees: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18 degrees ~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the radian (approximately).\r\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28alpha%29 ALIGN=MIDDLE  ALT=\"tan%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, approximately.\r\n" );
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document.write( "Then the apothem, which is the height of the single central triangle, is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.5%2A5%29%2F%28%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"%280.5%2A5%29%2F%28%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.5*3 = 7.5, approximately.\r\n" );
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document.write( "Then the area of one single central triangle is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%2A5%2A7.5 ALIGN=MIDDLE  ALT=\"%281%2F2%29%2A5%2A7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18.75.\r\n" );
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document.write( "Take it 10 times, and you will get the number 187.5 for the area.\r\n" );
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document.write( "Which number from the list is close to it?\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "It is very useful if somebody will show you how to do it.\r<BR>\n" );
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document.write( "At least once in your life !!\r<BR>\n" );
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document.write( "OK, it looks like I made some mistake, comparing with the more accurate answer of the other tutor.\r<BR>\n" );
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document.write( "Nevertheless, my error of 10% is allowable for such a crude estimation.\r<BR>\n" );
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