document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037659>Question 1037659</A>: <I><SPAN STYLE=\"word-break: break-all;\"> : Given the points A (0,0), B (4,3) and C (2,9), what is the measure of angle< ABC? I've graphed it but I'm not sure on how to actually find the angle or length  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652280 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the points A (0,0), B (4,3) and C (2,9), what is the measure of angle< ABC? I've graphed it but I'm not sure on how to actually find the angle or length <BR>\n" );
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document.write( "1 way to do this is to find the 3 side lengths, then use the Cosine Law to find the angle.<BR>\n" );
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document.write( "Another way is to use the Difference Formula for the tangents of 2 angles.<BR>\n" );
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document.write( "Find the slope of side AB and BC.<BR>\n" );
document.write( "The slope is the tangent of the angle between the line and the x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A-B%29+=+%28tan%28A%29+%2B+tan%28B%29%29%2F%281+%2B+tan%28A%29%2Atan%28B%29%29 ALIGN=MIDDLE  ALT=\"tan%28A-B%29+=+%28tan%28A%29+%2B+tan%28B%29%29%2F%281+%2B+tan%28A%29%2Atan%28B%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> tan = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m1+-+m2%29%2F%281+%2B+m1%2Am2%29 ALIGN=MIDDLE  ALT=\"%28m1+-+m2%29%2F%281+%2B+m1%2Am2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see from the graph that you use the negative tangent, ie, the angle is <BR>\n" );
document.write( "> 90 degs.<BR>\n" );
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document.write( "Wikipedia covers that well, look up \"Half Angle Formulas\"<BR>\n" );
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document.write( "email via the TY note for help or to check your work.<BR>\n" );
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