document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107297>Question 1107297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lines y=2x+4 and x+y=13 make angles of a^o and b^o with the  positive direction of the x-axis, as shown in the diagram.\r<BR>\n" );
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document.write( " (a)find the values of and b<BR>\n" );
document.write( " (b)hence find he acute angle between the two lines<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 #722300 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> slope of 2 has a tangent of 2 and an angle of 63.44 deg<BR>\n" );
document.write( "slope of -1 has an angle of 45 degrees.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C15%2C-10%2C12%2C2x%2B4%2C-x%2B13%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C15%2C-10%2C12%2C2x%2B4%2C-x%2B13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >the acute angle between them is 71.56 degrees. ANSWER\r<BR>\n" );
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document.write( "Can check by law of cosines if one wants to spend more time<BR>\n" );
document.write( "The sides are 15 along the axis <BR>\n" );
document.write( "The point of intersection is at (3, 10)<BR>\n" );
document.write( "the length of the side on the left of the graph is sqrt (125) and length of side on right side is sqrt (200)<BR>\n" );
document.write( "c^2=a^2+b^2-2ab cos C<BR>\n" );
document.write( "225=125+200-2(25000) cos C<BR>\n" );
document.write( "-100=-316.22 cos C<BR>\n" );
document.write( "cos C=0.3162<BR>\n" );
document.write( "C=71.56 degrees <BR>\n" );
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