document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210261>Question 1210261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Acute triangle ABC has \sin A = \dfrac{2}{5} and \sin B = \dfrac{2}{\sqrt{7}}. What is \sin C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851762 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=851762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "sin^2(A) + cos^2(A) = 1 ......... pythagorean trig identity<BR>\n" );
document.write( "(2/5)^2 + cos^2(A) = 1<BR>\n" );
document.write( "4/25 + cos^2(A) = 1<BR>\n" );
document.write( "cos^2(A) = 1 - 4/25<BR>\n" );
document.write( "cos^2(A) = 21/25<BR>\n" );
document.write( "cos(A) = sqrt(21/25) <BR>\n" );
document.write( "cos(A) = sqrt(21)/sqrt(25) <BR>\n" );
document.write( "cos(A) = sqrt(21)/5\r<BR>\n" );
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document.write( "sin^2(B) + cos^2(B) = 1<BR>\n" );
document.write( "(2/sqrt(7))^2 + cos^2(B) = 1<BR>\n" );
document.write( "4/7 + cos^2(B) = 1<BR>\n" );
document.write( "cos^2(B) = 1 - 4/7<BR>\n" );
document.write( "cos^2(B) = 3/7<BR>\n" );
document.write( "cos(B) = sqrt(3/7) \r<BR>\n" );
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document.write( "To summarize so far:<BR>\n" );
document.write( "sin(A) = 2/5<BR>\n" );
document.write( "cos(A) = sqrt(21)/5<BR>\n" );
document.write( "sin(B) = 2/sqrt(7)<BR>\n" );
document.write( "cos(B) = sqrt(3/7)\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "A+B+C = 180 degrees<BR>\n" );
document.write( "C = 180-(A+B)<BR>\n" );
document.write( "sin(C) = sin(180 - (A+B) )<BR>\n" );
document.write( "sin(C) = sin(A+B)  ........................................... use identity sin(180-x) = sin(x)<BR>\n" );
document.write( "sin(C) = sin(A)cos(B) + cos(A)sin(B) ......................... angle sum identity<BR>\n" );
document.write( "sin(C) = (2/5)*sqrt(3/7) + (sqrt(21)/5)*(2/sqrt(7))<BR>\n" );
document.write( "sin(C) = 2*sqrt(3)/(5*sqrt(7)) + 2*sqrt(21)/(5*sqrt(7))<BR>\n" );
document.write( "sin(C) = (2*sqrt(3) + 2*sqrt(21))/(5*sqrt(7))<BR>\n" );
document.write( "<font color=red>sin(C) = 2*(sqrt(3) + sqrt(21))/(5*sqrt(7)) exactly<BR>\n" );
document.write( "sin(C) = 0.9546817913107 approximately</font>\r<BR>\n" );
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document.write( "Another approach:<BR>\n" );
document.write( "sin(A) = 2/5<BR>\n" );
document.write( "A = arcsin(2/5)<BR>\n" );
document.write( "A = 23.5781784782 degrees approximately<BR>\n" );
document.write( "sin(B) = 2/sqrt(7)<BR>\n" );
document.write( "B = arcsin(2/sqrt(7))<BR>\n" );
document.write( "B = 49.10660535087 degrees approximately\r<BR>\n" );
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document.write( "A+B+C = 180<BR>\n" );
document.write( "C = 180-A-B<BR>\n" );
document.write( "C = 180-23.5781784782-49.10660535087<BR>\n" );
document.write( "C = 107.31521617093<BR>\n" );
document.write( "sin(C) = sin(107.31521617093)<BR>\n" );
document.write( "<font color=red>sin(C) = 0.9546817913107 approximately</font><BR>\n" );
document.write( "The drawback of this method is that you won't be able to determine the exact form in terms of square roots, as shown in the previous section. <BR>\n" );
document.write( "However, some teachers are perfectly fine with the answer in decimal form. <BR>\n" );
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