document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089694>Question 1089694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To the nearest tenth what is the altitude of an equilateral triangle whose sides measure 43 centimeters? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704037 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704037\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Start by drawing out an equilateral triangle ABC. Each point is a vertex of the triangle.<BR>\n" );
document.write( "Then plot another point D such that it is the midpoint of one of the sides. <BR>\n" );
document.write( "I made point D the midpoint of segment AB.<BR>\n" );
document.write( "In this case, the altitude is the segment from point C to point D.<BR>\n" );
document.write( "Let's call the altitude h for now (h for height) <BR>\n" );
document.write( "This is what the drawing should look like\r<BR>\n" );
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document.write( "Note how D splits AB into two equal halves. \r<BR>\n" );
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document.write( "We have these properties:\r<BR>\n" );
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document.write( "AD = DB<BR>\n" );
document.write( "AD = 21.5, DB = 21.5 (43/2 = 21.5)<BR>\n" );
document.write( "AD+DB = 21.5+21.5 = 43 = AB\r<BR>\n" );
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document.write( "Using that drawing above as reference, and focusing on triangle CDB, let's find what h must equal. \r<BR>\n" );
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document.write( "Because triangle CDB is a right triangle, we can use the pythagorean theorem\r<BR>\n" );
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document.write( "a = 21.5<BR>\n" );
document.write( "b = h<BR>\n" );
document.write( "c = 43\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the pythagorean theorem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2821.5%29%5E2+%2B+h%5E2+=+%2843%29%5E2 ALIGN=MIDDLE  ALT=\"%2821.5%29%5E2+%2B+h%5E2+=+%2843%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given values\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=462.25+%2B+h%5E2+=+1849 ALIGN=MIDDLE  ALT=\"462.25+%2B+h%5E2+=+1849\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=462.25+%2B+h%5E2+-+462.25+=+1849+-+462.25 ALIGN=MIDDLE  ALT=\"462.25+%2B+h%5E2+-+462.25+=+1849+-+462.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 462.25 from both sides \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+=+1386.75 ALIGN=MIDDLE  ALT=\"h%5E2+=+1386.75\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28h%5E2%29+=+sqrt%281386.75%29 ALIGN=MIDDLE  ALT=\"sqrt%28h%5E2%29+=+sqrt%281386.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+37.2390923627309 ALIGN=MIDDLE  ALT=\"h+=+37.2390923627309\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compute the square root (use a calculator)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+37.2 ALIGN=MIDDLE  ALT=\"h+=+37.2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Round to the nearest tenth\r<BR>\n" );
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document.write( "<font color=red>The altitude is roughly 37.2 cm</font>\r<BR>\n" );
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