document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023319>Question 1023319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given square pyramid: square ABCD with base side AB = 2cm, and height EO = 3cm. Find the exact length of AC and the exact length of EC.<BR>\n" );
document.write( "F is the midpoint of CB. Find the exact slant height EF.<BR>\n" );
document.write( "Thanks for any help!:) Thank you so much, I'm having a lot of trouble with this question! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638837 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=638837\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AC is a diagonal of the square base.<BR>\n" );
document.write( "as such it's length would be sqrt(2^2 + 2^2) = sqrt(8).<BR>\n" );
document.write( "the diagonal AC forms a triangle AEC of which EO is the altitude.<BR>\n" );
document.write( "this triangle AEC, with its altitude of EO, forms 2 right triangles.<BR>\n" );
document.write( "they are triangle AEO and triangle EOC.<BR>\n" );
document.write( "the height of these triangles is 3.<BR>\n" );
document.write( "the base of these triangles is sqrt(8)/2.<BR>\n" );
document.write( "the hypotenuse of these triangles is equal to sqrt(3^2 + (sqrt(8)/2)^2).<BR>\n" );
document.write( "this becomes sqrt(9 + 8/4) which becomes sqrt(36/4 + 8/4) which becomes sqrt(44/4) which becomes sqrt(44)/2 which becomes sqrt(4*11)/2 which becomes 2*sqrt(11)/2 which becomes sqrt(11).\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "length of AC is sqrt(8).<BR>\n" );
document.write( "length of EC is sqrt(11).\r<BR>\n" );
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document.write( "the diagram below should help you visualize what's happening.\r<BR>\n" );
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