document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165933>Question 165933</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with a question could someone please help??\r<BR>\n" );
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document.write( "Find the length, to the nearest tenth, of the apothem of a regular octogon whose sides are each 10 inches long? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122311 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=122311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question:  Find the length, to the nearest tenth, of the apothem of a regular octagon whose sides are each 10 inches long.<BR>\n" );
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document.write( "Answer:  The center of a regular polygon is equidistant from the vertices.  The apothem is the distance from the center to a side.  A central angle of a regular polygon has its vertex at the center, and its sides pass through consecutive vertices.<BR>\n" );
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document.write( "Each central angle measure of a regular n-gon is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2Fn ALIGN=MIDDLE  ALT=\"360%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees.<BR>\n" );
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document.write( "Draw the octagon.  Draw an isosceles triangle with its vertex at the center of the octagon.  The central angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%2F8 ALIGN=MIDDLE  ALT=\"360%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or 45 degrees.  Draw a segment that bisects the central angle and the side of the polygon to form a right triangle.<BR>\n" );
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document.write( "Use the tangent ratio to find the apothem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan22.5=5%2Fa ALIGN=MIDDLE  ALT=\"tan22.5=5%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The tangent of an angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22tangent_angle%22=%22opposite_leg%22%2F%22adjacent_leg%22 ALIGN=MIDDLE  ALT=\"%22tangent_angle%22=%22opposite_leg%22%2F%22adjacent_leg%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "*NOTE: you use 22.5 because you bisected the central angle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%285%2F%28tan22.5%29%29 ALIGN=MIDDLE  ALT=\"a=%285%2F%28tan22.5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Solve for a.<BR>\n" );
document.write( "a=8.96295... inches  Round to the nearest tenth<BR>\n" );
document.write( "a=9.0 inches<BR>\n" );
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document.write( "Check out my website by clicking on my profile.<BR>\n" );
document.write( "You can find a scanned picture of my work for this problem.  Just go to the solutions page and click on \"apothem\"<BR>\n" );
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document.write( "contact justin.sheppard.tech@hotmail.com with any questions\r<BR>\n" );
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