document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888882>Question 888882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a regular pentagon is inscribed in a circle whose radius is 18cm. find the perimeter of the pentagon </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #537726 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the radius of the circle is 18 cm.<BR>\n" );
document.write( "this radius is also the equal sides of the isosceles triangle formed.<BR>\n" );
document.write( "you want to find the length of the base of the triangle formed.<BR>\n" );
document.write( "that will allow you to find the perimeter.<BR>\n" );
document.write( "in order to find the length of the base, you need to find the interior angles of one of the triangles formed in the pentagon.<BR>\n" );
document.write( "since all of the triangles formed are congruent in a regular pentagon, if you find one, you've found them all.\r<BR>\n" );
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document.write( "the central angle in each triangle formed from the center of the pentagon to the vertex of the pentagon is equal to 360 / n, where n = the number of sides, which is 5 in the case of a pentagon.\r<BR>\n" );
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document.write( "360 / 5 = 72 degrees.<BR>\n" );
document.write( "that's the central angle of each of the triangles formed.\r<BR>\n" );
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document.write( "since the triangles are isosceles, the base angles are equal to (180 - 72) / 2 which makes each base angle of one of the triangles in the pentagon equal to 54.\r<BR>\n" );
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document.write( "drop a perpendicular from the central angle of one triangle to the base of that triangle and you form two congruent right triangles, each of which has a central angle of 36 degrees and a right angle of 90 degrees and a leg angle of 54 degrees.\r<BR>\n" );
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document.write( "the following picture shows you what i mean.<BR>\n" );
document.write( "the pentagon is ABCDE.<BR>\n" );
document.write( "one of the triangles formed is AOE.<BR>\n" );
document.write( "the perpendicular that is dropped from the central angle is OF.<BR>\n" );
document.write( "OAF and OEF are base angles of the two right triangles formed.<BR>\n" );
document.write( "the central angle of 72 degrees is split into two angles of 36 degrees apiece.<BR>\n" );
document.write( "The right triangle of OEF was used to calculate FE which is equal to one half the length of the side of the pentagon.<BR>\n" );
document.write( "Two times that is the length of the side of the pentagon.<BR>\n" );
document.write( "FE and AF are referenced as x in the equation.<BR>\n" );
document.write( "AE is referenced as 2x in the equation.<BR>\n" );
document.write( "x is equal to 10.58...<BR>\n" );
document.write( "2x is equal to 21.16...<BR>\n" );
document.write( "5 * 2x is equal to 105.80...<BR>\n" );
document.write( "105.l80 is referenced as P.<BR>\n" );
document.write( "that's your perimeter.\r<BR>\n" );
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