document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846879>Question 846879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of the triangle with vertices (0, 0), (5, 3) and (2, 6). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509980 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C10%2C-2%2C10%2Cgrid%281%29%2C%0D%0Acircle%280%2C0%2C0.2%29%2C%0D%0Acircle%285%2C3%2C0.2%29%2C%0D%0Acircle%282%2C6%2C0.2%29%2C%0D%0Aline%280%2C0%2C5%2C3%29%2C%0D%0Aline%285%2C3%2C2%2C6%29%2C%0D%0Aline%282%2C6%2C0%2C0%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We need to find the altitude of the triangle.<BR>\n" );
document.write( "Calculate the angle that the (0,0) to (5,3) line makes with the x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=3%2F5 ALIGN=MIDDLE  ALT=\"tan%28theta%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=0.54042 ALIGN=MIDDLE  ALT=\"theta=0.54042\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians<BR>\n" );
document.write( "Calculate the angle that the (0,0) to (2,6) line makes with the x-axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29=6%2F2 ALIGN=MIDDLE  ALT=\"tan%28theta%29=6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta=1.24906 ALIGN=MIDDLE  ALT=\"theta=1.24906\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians<BR>\n" );
document.write( "So then the angle between the (2,6) line and the (5,3) line is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.24906-0.54042=0.708626 ALIGN=MIDDLE  ALT=\"1.24906-0.54042=0.708626\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians <BR>\n" );
document.write( "The sine of that angle and the hypotenuse would give us the altitude of the triangle.<BR>\n" );
document.write( "The hypotenuse is the distance from (0,0) to (2,6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=%282-0%29%5E2%2B%286-0%29%5E2=40 ALIGN=MIDDLE  ALT=\"H%5E2=%282-0%29%5E2%2B%286-0%29%5E2=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=sqrt%2840%29 ALIGN=MIDDLE  ALT=\"H=sqrt%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=sqrt%2840%29%2Asin%280.708626%29 ALIGN=MIDDLE  ALT=\"A=sqrt%2840%29%2Asin%280.708626%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The base of the triangle is the distance from (0,0) to (5,3),<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5E2=5%5E2%2B3%5E2=34 ALIGN=MIDDLE  ALT=\"B%5E2=5%5E2%2B3%5E2=34\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=sqrt%2834%29 ALIGN=MIDDLE  ALT=\"B=sqrt%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then the area of the triangle is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D=%281%2F2%29A%2AB=%281%2F2%29sqrt%2840%29sqrt%2834%29sin%280.708626%29 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=%281%2F2%29A%2AB=%281%2F2%29sqrt%2840%29sqrt%2834%29sin%280.708626%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D=%281%2F2%29A%2AB=%281%2F2%29sqrt%281360%29%2A0.650791 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=%281%2F2%29A%2AB=%281%2F2%29sqrt%281360%29%2A0.650791\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D=12 ALIGN=MIDDLE  ALT=\"A%5Bt%5D=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );