document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143958>Question 143958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do you solve for an altitude?<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 #104792 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20855)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=104792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=altitude ALIGN=MIDDLE  ALT=\"altitude\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a triangle is a straight line through a vertex and perpendicular to ( forming a right angle with) the opposite side. This opposite side is called the base of the altitude.\r<BR>\n" );
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document.write( "The length of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=altitude ALIGN=MIDDLE  ALT=\"altitude\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the distance between the base and the vertex.\r<BR>\n" );
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document.write( "Calculating the area of a triangle is an elementary problem encountered often in many different situations. \r<BR>\n" );
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document.write( "The best known, and simplest formula is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281%2F2%29+bh ALIGN=MIDDLE  ALT=\"S=%281%2F2%29+bh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > is area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the base of the triangle, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height or altitude of the triangle. \r<BR>\n" );
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document.write( "If you know the area, you can calculate the height or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=altitude ALIGN=MIDDLE  ALT=\"altitude\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%281%2F2%29+bh ALIGN=MIDDLE  ALT=\"S=%281%2F2%29+bh\"   DISABLED_style= \"max-width:90%; height:auto;\" >……..solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S=bh ALIGN=MIDDLE  ALT=\"2S=bh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2S%2Fb ALIGN=MIDDLE  ALT=\"h=2S%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Right Triangle Altitude: The measure of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=altitude ALIGN=MIDDLE  ALT=\"altitude\"   DISABLED_style= \"max-width:90%; height:auto;\" > drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.<BR>\n" );
document.write( "In terms of our triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABC ALIGN=MIDDLE  ALT=\"ABC\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this theorem simply states what we have already shown: \r<BR>\n" );
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document.write( "if the altitude has intersection point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a hypotenuse, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=+sqrt%28CD%2ADB%29 ALIGN=MIDDLE  ALT=\"AD=+sqrt%28CD%2ADB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=altitude ALIGN=MIDDLE  ALT=\"altitude\"   DISABLED_style= \"max-width:90%; height:auto;\" > drawn from the right angle of our right triangle to its hypotenuse, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DB ALIGN=MIDDLE  ALT=\"DB\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the two segments of the hypotenuse.\r<BR>\n" );
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