document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916112>Question 916112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given sinA:4/5, cosB=5/13 both A and B in quadrant I, find tan(A+B) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555927 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=555927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given sinA:4/5, cosB=5/13 both A and B in quadrant I, find tan(A+B)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "sinA=4/5<BR>\n" );
document.write( "cosA=3/5(working with a 3-4-5 reference right triangle)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "cosB=5/13<BR>\n" );
document.write( "sinB=12/13(working with a 5-12-13 reference right triangle)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "sin(A+B)=sinAcosB+cosAsinB=4/5*5/13+3/5*12/13=20/65+36/65=56/65<BR>\n" );
document.write( "cos(A+B)=cosAcosB-sinAsinB=3/5*5/13-4/5*12/13=15/65-48/65=-33/65<BR>\n" );
document.write( "tan(A+B)=sin(A+B)/cos(A+B)=-56/33<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "sinA=4/5<BR>\n" );
document.write( "A=53.13&#730;<BR>\n" );
document.write( "cosB=5/13<BR>\n" );
document.write( "B=67.38&#730;<BR>\n" );
document.write( "A+B=53.13+67.38=120.51&#730;<BR>\n" );
document.write( "tan(A+B)=tan(120.51&#730;)=-1.6969...<BR>\n" );
document.write( "as calculated: tan(A+B)=-56/33=-1.6969... </SPAN>\n" );
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