document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199591>Question 1199591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im a triangle ABC.<BR>\n" );
document.write( "Cos A/a = Cos B/b = Cos C/c, and a = 2. It is possible to compute the area of the<BR>\n" );
document.write( "triangle, (Hint: compare the problem data with the Law of the Sines, compute ratios between the sines and cosines of the angles)<BR>\n" );
document.write( "A) sqrt3/4<BR>\n" );
document.write( "B) sqrt3/2<BR>\n" );
document.write( "C) sqrt3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833553 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "cos(A)/a = cos(B)/b = cos(C)/c<BR>\n" );
document.write( "cos(A)/a = cos(B)/b<BR>\n" );
document.write( "cos(A)/cos(B) = a/b\r<BR>\n" );
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document.write( "Use the law of sines to apply similar steps:<BR>\n" );
document.write( "sin(A)/a = sin(B)/b = sin(C)/c<BR>\n" );
document.write( "sin(A)/a = sin(B)/b<BR>\n" );
document.write( "sin(A)/sin(B) = a/b\r<BR>\n" );
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document.write( "We can see that:<BR>\n" );
document.write( "cos(A)/cos(B) = a/b<BR>\n" );
document.write( "cos(A)/cos(B) = sin(A)/sin(B)<BR>\n" );
document.write( "which can be rearranged into<BR>\n" );
document.write( "sin(B)/cos(B) = sin(A)/cos(A)<BR>\n" );
document.write( "tan(B) = tan(A)<BR>\n" );
document.write( "B = A<BR>\n" );
document.write( "A = B\r<BR>\n" );
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document.write( "Follow a similar chain of logic to conclude that B = C.\r<BR>\n" );
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document.write( "We have A = B and B = C, so A = C<BR>\n" );
document.write( "All three angles are the same measure. <BR>\n" );
document.write( "A+B+C = 180<BR>\n" );
document.write( "A+A+A = 180<BR>\n" );
document.write( "3A = 180<BR>\n" );
document.write( "A = 180/3<BR>\n" );
document.write( "A = 60<BR>\n" );
document.write( "Each angle is 60 degrees.<BR>\n" );
document.write( "The triangle is equilateral.\r<BR>\n" );
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document.write( "Area of equilateral triangle with side length 's'<BR>\n" );
document.write( "Area = 0.25*s^2*sqrt(3)<BR>\n" );
document.write( "Area = 0.25*2^2*sqrt(3)<BR>\n" );
document.write( "Area = sqrt(3)\r<BR>\n" );
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document.write( "Answer: <font color=red>C)  sqrt(3)</font><BR>\n" );
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