document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083349>Question 1083349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the acute angle between the following straight lines \r<BR>\n" );
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document.write( "y=(0.5)(x)+1   and y=-(1/3)(x)+2   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697591 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the angle is 45 degrees as best i can see.\r<BR>\n" );
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document.write( "i believe you can just go by the slope.\r<BR>\n" );
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document.write( "the y-intercept determines where the intersection of the 2 lines will be but it doesn't change the angle between the lines.\r<BR>\n" );
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document.write( "i tested this out and it appears to be correct.\r<BR>\n" );
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document.write( "a slope of .5 means the opposite side of the right triangle formed is 1/2 the length of the adjacent side.\r<BR>\n" );
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document.write( "if the adjacent side is equal to 1, then the opposite side is equal to 1/2 and the tangent of the angle is equal to 1/2 / 1 which is equal to 1/2 which gives you an angle of 26.56505118 when you find the arc tangent of 1/2.\r<BR>\n" );
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document.write( "a slope of -1/3 means the opposite side is 1/3 the length of the adjacent side.\r<BR>\n" );
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document.write( "if the adjacent side is equal to 1, then the opposite side is equal to -1/3 and the tangent of the angle is equal to -1/3 / 1 which gives you an angle of -18.43494882 degrees.\r<BR>\n" );
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document.write( "add these angles together and you get an angle of 45 degrees between the two lines.\r<BR>\n" );
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document.write( "these are vertical angles of the intersection.\r<BR>\n" );
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document.write( "the other vertical angles of the intersection will be 180 - 45 = 135 degrees.\r<BR>\n" );
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document.write( "45 degrees are the acute vertical angles.\r<BR>\n" );
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document.write( "135 degrees are the obtuse vertical angles.\r<BR>\n" );
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document.write( "the graph of these two lines looks like this.\r<BR>\n" );
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