document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=220233>Question 220233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the altitude of an  equilateral triangle that has side lengths of 4y. Express your answer in simplest radical form. <BR>\n" );
document.write( "I am a homeschooling mom and don't remeber how to do this. Our book doesnt help either. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #165379 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=165379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If you construct an altitude of an equilateral triangle, then the altitude forms a right angle with the base.  That means that you have now formed two 30-60-90 triangles, i.e. right triangles where the hypotenuse is one side of the equilateral triangle and the short leg is exactly one-half the measure of the hypotenuse.  Now having a hypotenuse of 4 and a short leg of 2, we can use Pythagoras to calculate the measure of the long leg which is the same as the altitude of the equilateral triangle:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ \sqrt{c^2 - a^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ =\ \sqrt{4^2 - 2^2}\ =\ \sqrt{12}\ =\ \sqrt{4\cdot3}\ =\ \sqrt{4}\cdot\sqrt{2}\ =\ 2\cdot\sqrt{3}\">\r<BR>\n" );
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document.write( "In general, if the measure of the length of a side of an equilateral triangle is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s\">, then the measure of an altitude is:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s\cdot\frac{\sqrt{3}}{2}\">\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" );
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