document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975346>Question 975346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the height of an scalene triangle, where not angle degrees are provided, only the following side dimensions?: The base=14cm, the longest side=15cm and the shortest side=13cm </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597113 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=597113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The formula for the height of a scalene triangle is dependent on the measure of the base to which you want to measure the height (which you did not specify) and the area of the triangle.\r<BR>\n" );
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document.write( "So the first thing we are faced with is the problem of finding the area of the triangle knowing the measures of the three sides.  Fortunately, Pythagoras wasn't the only old Greek guy who knew something about Geometry.  Heron (or Hero) of Alexandria left us with the following formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \sqrt{s(s\ -\ a)(s\ -\ b)(s\ - c)}\">\r<BR>\n" );
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document.write( "Ok, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\"> are the measures of the sides, but what is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s\">?\r<BR>\n" );
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document.write( "Actually, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s\"> is simply the semi-perimeter, which is to say the perimeter divided by 2.  In the case of your triangle, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 15\ +\ 14\ +\ 13\ =\ 42\"> and half of that is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 21\">.  Now we can calculate the area.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \sqrt{21(21\ -\ 15)(21\ -\ 14)(21\ - 13)}\">\r<BR>\n" );
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document.write( "I'll leave that arithmetic up to you.\r<BR>\n" );
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document.write( "Once you have the area, and have decided which of the three sides you want to consider the base, you can calculate the height with respect to that base using:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h_i\ =\ 2\frac{A}{b_i}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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