document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149171>Question 149171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7. The altitude of a regular triangular pyramid is the segment connecting a vertex to the centroid of the opposite face. A regular triangular pyramid has edges of length 6 inches. How tall is such a pyramid, to the nearest hundredth of an inch? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109433 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=109433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's draw the pyramid (note: my drawings are not to scale).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/pyramid.jpg\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "If we just look at the base, we get something like this (Note: The hypotenuse was found through pythagorean's theorem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%5E2%2B6%5E2%29=sqrt%2836%2B36%29=sqrt%2872%29=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%286%5E2%2B6%5E2%29=sqrt%2836%2B36%29=sqrt%2872%29=6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/pyramid_base.jpg\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "Now take half of the hypotenuse to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This figure will form the leg of the triangle. Now let's one half of a triangular cross section to get this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/upright_triangle.jpg\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "From the drawing, we can see that legs are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > while the hypotenuse is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So to find \"h\", we need to use pythagorean's theorem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2%2B%283%2Asqrt%282%29%29%5E2=6%5E2 ALIGN=MIDDLE  ALT=\"h%5E2%2B%283%2Asqrt%282%29%29%5E2=6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=h ALIGN=MIDDLE  ALT=\"a=h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"b=3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=6 ALIGN=MIDDLE  ALT=\"c=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2%2B%283%2Asqrt%282%29%29%5E2=36 ALIGN=MIDDLE  ALT=\"h%5E2%2B%283%2Asqrt%282%29%29%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 6 to get 36.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2%2B18=36 ALIGN=MIDDLE  ALT=\"h%5E2%2B18=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Asqrt%282%29%29%5E2=%283%2Asqrt%282%29%29%283%2Asqrt%282%29%29=%283%2A3%29%2A%28sqrt%282%29%2Asqrt%282%29%29=9%2A2=18 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=36-18 ALIGN=MIDDLE  ALT=\"h%5E2=36-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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=18 ALIGN=MIDDLE  ALT=\"h%5E2=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%2818%29 ALIGN=MIDDLE  ALT=\"h=sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides. Note: only the positive square root is considered.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"h=3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "So the height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"h=3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=4.24264 ALIGN=MIDDLE  ALT=\"h=4.24264\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the height of the pyramid to the nearest hundredth of an inch is 4.25 inches<BR>\n" );
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