document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927493>Question 927493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two sides of a triangle measure 80 cm and 64 cm. The area of the triangle is 2,262 cm. Find the third side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563034 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two sides of a triangle measure 80 cm and 64 cm. The area of the triangle is 2,262 cm [sic] it's sq cm. Find the third side.<BR>\n" );
document.write( "============<BR>\n" );
document.write( "Area = b*h/2<BR>\n" );
document.write( "b = 80<BR>\n" );
document.write( "A = angle between the given sides<BR>\n" );
document.write( "h = 64*sin(A)<BR>\n" );
document.write( "2262 = 80*64*sin(A)/2 = 2560*sin(A)<BR>\n" );
document.write( "sin(A) = 2262/2560 =~ 0.883594<BR>\n" );
document.write( "A =~ 62.1 degs<BR>\n" );
document.write( "----<BR>\n" );
document.write( "c = 3rd side<BR>\n" );
document.write( "c^2 = a^2 + b^2 - 2abcos(A)<BR>\n" );
document.write( "c^2 = 80^2 + 64^2 - 2*80*64*cos(62.1)<BR>\n" );
document.write( "c^2 = 6400 + 4096 - 10240*0.468254 = ~5701<BR>\n" );
document.write( "c = 75.5<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Check using Heron's Law<BR>\n" );
document.write( "s = (80+64+75.5)/2 = 109.75<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 ALIGN=MIDDLE  ALT=\"Area+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+sqrt%28109.75%2A29.75%2A45.75%2A34.25%29%29 ALIGN=MIDDLE  ALT=\"Area+=+sqrt%28109.75%2A29.75%2A45.75%2A34.25%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Area = 2261.89<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "It's surprising, I've been doing this stuff for 55 years or so, and never seen a problem like this one. </SPAN>\n" );
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