document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197857>Question 1197857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC angle m < A is 45 degrees,  angle m < B=30 degrees, and side a=10. What is the side b of the trangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831301 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=831301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I have edited your question to add in the necessary spaces, so that the full question is visible.<BR>\n" );
document.write( "The issue is that the less than sign needs space on both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question: <BR>\n" );
document.write( "In triangle ABC angle m < A is 45 degrees,  angle m < B=30 degrees, and side a=10. What is the side b of the triangle?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solution: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It helps to draw out what we know so far.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_117.png\"><BR>\n" );
document.write( "Convention is to have the uppercase letters represent angles, while the lowercase letters are side lengths.<BR>\n" );
document.write( "Angle A is opposite side 'a'<BR>\n" );
document.write( "Angle B is opposite side 'b'<BR>\n" );
document.write( "Angle C is opposite side 'c'\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the law of sines to determine side b<BR>\n" );
document.write( "sin(A)/a = sin(B)/b<BR>\n" );
document.write( "b*sin(A) = a*sin(B) .... cross multiply<BR>\n" );
document.write( "b = a*sin(B)/sin(A) .... divide both sides by sin(A)<BR>\n" );
document.write( "b = 10*sin(30)/sin(45)<BR>\n" );
document.write( "<font color=red>b = 7.07106781186548 approximately</font><BR>\n" );
document.write( "Round that however your teacher instructs.<BR>\n" );
document.write( "Make sure your calculator is in degree mode.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Extra info:<BR>\n" );
document.write( "If you want to find side c, then you'll need to find angle C first.<BR>\n" );
document.write( "Use the fact that the interior angles of a triangle add to 180, so A+B+C = 180<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );