document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168637>Question 168637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the perimeter of the equilateral traiangle inscribed in a circle of radius 20.0 inches </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124399 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+400%2C+300%2C+-45%2C+45%2C+-45%2C+45%2C%0D%0A%0D%0A++locate%280%2C0%2Co%28A%29%29%2C%0D%0A++circle%28+0%2C0%2C+20+%29%2C+%0D%0Alocate%2814%2C-18%2C%28C%29%29%2C%0D%0Aline%280%2C0%2C14%2C-18%29%2C%0D%0Alocate%280%2C-18%2C%28B%29%29%2C%0D%0Aline%280%2C0%2C0%2C-18%29%2C%0D%0Atriangle%28+14%2C-18%2C-14%2C-18%2C0%2C27%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "AC is equal to the radius 20. <BR>\n" );
document.write( "We know that angle C is half of the original angle of the original equilateral triangle(60) ....so C is 60/2=30.   ABC is a right triangle so we know that angle A is a 60 degree angle  180-90-30=60<BR>\n" );
document.write( ":<BR>\n" );
document.write( "BC is equal to 1/2 of the entire side of the equilateral triangle \r<BR>\n" );
document.write( "\n" );
document.write( "and we know that sine 60 degrees =BC/20(hypothenuse of the ABC)--->solving for BC=20(sine60degrees)=17.32<BR>\n" );
document.write( ":<BR>\n" );
document.write( "now if we double BC we will have the entire length of one side of the equilateral triangle ( 17.32(2)=34.64)---> and since all sides are equal the Perimeter is three times this length. 34.64(3)=103.92 inches </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );