document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184155>Question 1184155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a triangle if CosA/a = CosB/b = CosC/c and if a = 2 then find the area of triangle ABC? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814722 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By hypothesis, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CosA%2Fa+=+CosB%2Fb+=+CosC%2Fc ALIGN=MIDDLE  ALT=\"CosA%2Fa+=+CosB%2Fb+=+CosC%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since the triangle also obeys the Sine Law, we also have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinA%2Fa+=+SinB%2Fb+=+SinC%2Fc ALIGN=MIDDLE  ALT=\"sinA%2Fa+=+SinB%2Fb+=+SinC%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CosA%2Fa+=+CosB%2Fb ALIGN=MIDDLE  ALT=\"CosA%2Fa+=+CosB%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinA%2Fa+=+SinB%2Fb ALIGN=MIDDLE  ALT=\"sinA%2Fa+=+SinB%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cos%5E2A%2Fa%5E2+=+Cos%5E2B%2Fb%5E2 ALIGN=MIDDLE  ALT=\"Cos%5E2A%2Fa%5E2+=+Cos%5E2B%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Sin%5E2A%2Fa%5E2+=+Sin%5E2B%2Fb%5E2 ALIGN=MIDDLE  ALT=\"Sin%5E2A%2Fa%5E2+=+Sin%5E2B%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By adding corresponding sides of the last two equations, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa%5E2+=+1%2Fb%5E2 ALIGN=MIDDLE  ALT=\"1%2Fa%5E2+=+1%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which implies that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b ALIGN=MIDDLE  ALT=\"a+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Similarly, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CosA%2Fa+=+CosC%2Fc ALIGN=MIDDLE  ALT=\"CosA%2Fa+=+CosC%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sinA%2Fa+=+SinC%2Fc ALIGN=MIDDLE  ALT=\"sinA%2Fa+=+SinC%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+c ALIGN=MIDDLE  ALT=\"a+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore, the triangle is actually an isosceles triangle, each side having a measure of a = 2 units.\r<BR>\n" );
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document.write( "Hence its area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+%281%2F2%29%2Aa%2A%28%28sqrt%283%29%2F2%29%2Aa%29+=+%28sqrt%283%29%2F4%29%2Aa%5E2+=+%28sqrt%283%29%2F4%29%2A2%5E2+=+highlight%28sqrt%283%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > square units. </SPAN>\n" );
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