document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035292>Question 1035292</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a triangle ABC, angle A = 2 angle B. How would you prove that BC² = AC² + AB × AC? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649954 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=649954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use law of sines. Here <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \sin A = \sin 2B = 2 \sin B \cos B\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{\sin A}{BC} = \frac{\sin B}{AC} \Leftrightarrow \frac{2 \sin B \cos B}{BC} = \frac{\sin B}{AC} \Leftrightarrow \frac{2 \cos B}{BC} = \frac{1}{AC}\">\r<BR>\n" );
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document.write( "Cross-multiplying, this is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \cos B = \frac{BC}{2 \cdot AC}\">.\r<BR>\n" );
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document.write( "Applying the law of cosines, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large AC^2 = AB^2 + BC^2 - 2AB \cdot BC \cos B\">\r<BR>\n" );
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document.write( "This is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \cos B = \frac{AB^2 + BC^2 - AC^2}{2 AB \cdot BC}\">.\r<BR>\n" );
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document.write( "Substituting we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{AB^2 + BC^2 - AC^2}{2 AB \cdot BC} = \frac{BC}{2 \cdot AC}\">\r<BR>\n" );
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document.write( "You can then solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large BC^2\">. However I don't think what I got matches with the expression you provided (either I messed up my algebra or the question you typed is incorrect). </SPAN>\n" );
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