document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927442>Question 927442</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.the sides of a triangle measures 20cm, 25,cm and 30 cm.<BR>\n" );
document.write( "Find the length of the altitude to the shortest side.<BR>\n" );
document.write( "Find the length of the median to the longest side.<BR>\n" );
document.write( "find the length of the angle bisector of the smallest angle.<BR>\n" );
document.write( "find the length of the line segment joining the midpoints of the 20-cm and 30-cm sides. \r<BR>\n" );
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document.write( "THANK YOUU.<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 #562999 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=562999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.the sides of a triangle measures<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=20cm ALIGN=MIDDLE  ALT=\"a=20cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c=25cm ALIGN=MIDDLE  ALT=\"+c=25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=30cm ALIGN=MIDDLE  ALT=\"b=30cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "find the length of the angle bisector of the smallest angle.<BR>\n" );
document.write( "find the length of the line segment joining the midpoints of the 20-cm and 30-cm sides.\r<BR>\n" );
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document.write( "Find the length of the altitude to the shortest side:\r<BR>\n" );
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document.write( "You know the lengths of 3 sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=20cm ALIGN=MIDDLE  ALT=\"a=20cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c=25cm ALIGN=MIDDLE  ALT=\"+c=25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=30cm ALIGN=MIDDLE  ALT=\"b=30cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h    is  the altitude\r<BR>\n" );
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document.write( "Use Heron's formula to find out the area\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+sqrt%28+s+%28+s-a%29+%28+s-b%29+%28+s-c%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%28+s+%28+s-a%29+%28+s-b%29+%28+s-c%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........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;\" >= semi-perimeter and a,b, and c are side lengths\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+%2820cm%2B25cm%2B30cm%29%2F2=75cm%2F2=37.5cm ALIGN=MIDDLE  ALT=\"s+=+%2820cm%2B25cm%2B30cm%29%2F2=75cm%2F2=37.5cm\"   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=A+=+sqrt%2837.5+%28+37.5-20%29+%2837.5-25%29+%2837.5-30%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%2837.5+%28+37.5-20%29+%2837.5-25%29+%2837.5-30%29%29\"   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=A+=+sqrt%2837.5+%28+17.5%29+%2812.5%29+%287.5%29%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%2837.5+%28+17.5%29+%2812.5%29+%287.5%29%29\"   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=A+=+sqrt%2861523.4375%29 ALIGN=MIDDLE  ALT=\"A+=+sqrt%2861523.4375%29\"   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=A+=+248.04 ALIGN=MIDDLE  ALT=\"A+=+248.04\"   DISABLED_style= \"max-width:90%; height:auto;\" > then use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=248.04+=+%281%2F2%29+%2A+20%2A+h ALIGN=MIDDLE  ALT=\"248.04+=+%281%2F2%29+%2A+20%2A+h\"   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=248.04+=+10%2A+h ALIGN=MIDDLE  ALT=\"248.04+=+10%2A+h\"   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+=+24.8+cm ALIGN=MIDDLE  ALT=\"h+=+24.8+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER \r<BR>\n" );
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document.write( "Find the length of the median to the longest side:\r<BR>\n" );
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document.write( "the longest side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=30+cm ALIGN=MIDDLE  ALT=\"b=30+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Draw 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;\" >, with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+25cm ALIGN=MIDDLE  ALT=\"AB+=+25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+20cm ALIGN=MIDDLE  ALT=\"BC+=+20cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+30cm ALIGN=MIDDLE  ALT=\"AC+=+30cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using law of cosines, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2+%2B+b%5E2-2%2Aa%2Ab%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2+%2B+b%5E2-2%2Aa%2Ab%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%5E2+=+20%5E2+%2B+30%5E2-2%2A20%2A30%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"25%5E2+=+20%5E2+%2B+30%5E2-2%2A20%2A30%2Acos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625=+400%2B+900-1200%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"625=+400%2B+900-1200%2Acos%28C%29\"   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=625=+1300-1200%2Acos%28C%29 ALIGN=MIDDLE  ALT=\"625=+1300-1200%2Acos%28C%29\"   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=1200%2Acos%28C%29=+1300-625 ALIGN=MIDDLE  ALT=\"1200%2Acos%28C%29=+1300-625\"   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=1200%2Acos%28C%29=+675 ALIGN=MIDDLE  ALT=\"1200%2Acos%28C%29=+675\"   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=cos%28C%29=+675%2F1200 ALIGN=MIDDLE  ALT=\"cos%28C%29=+675%2F1200\"   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=cos%28C%29=+0.5625 ALIGN=MIDDLE  ALT=\"cos%28C%29=+0.5625\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Draw median from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now we have triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCM ALIGN=MIDDLE  ALT=\"BCM\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+20cm ALIGN=MIDDLE  ALT=\"BC+=+20cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CM+=+15cm ALIGN=MIDDLE  ALT=\"CM+=+15cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We will find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM ALIGN=MIDDLE  ALT=\"BM\"   DISABLED_style= \"max-width:90%; height:auto;\" > using law of cosines:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM%5E2=+BC%5E2+%2B+CM%5E2+-+2+%28BC%29%28+CM%29+cos%28C%29 ALIGN=MIDDLE  ALT=\"BM%5E2=+BC%5E2+%2B+CM%5E2+-+2+%28BC%29%28+CM%29+cos%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM%5E2=+20%5E2+%2B+15%5E2-+2+%2820%29%2815%29+%280.5625%29 ALIGN=MIDDLE  ALT=\"BM%5E2=+20%5E2+%2B+15%5E2-+2+%2820%29%2815%29+%280.5625%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM%5E2=+400%2B+225+-+337.5 ALIGN=MIDDLE  ALT=\"BM%5E2=+400%2B+225+-+337.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM%5E2=+287.5 ALIGN=MIDDLE  ALT=\"BM%5E2=+287.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Median  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM=+sqrt%28287.5%29 ALIGN=MIDDLE  ALT=\"BM=+sqrt%28287.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM=16.96cm ALIGN=MIDDLE  ALT=\"BM=16.96cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER\r<BR>\n" );
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document.write( "find the length of the angle bisector of the smallest angle.\r<BR>\n" );
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document.write( "Then the length of the angle bisector <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given by:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=%28ac%2F%28a%2Bc%29%5E2%29%28%28a%2Bc%29%5E2-b%5E2%29+ ALIGN=MIDDLE  ALT=\"d%5E2=%28ac%2F%28a%2Bc%29%5E2%29%28%28a%2Bc%29%5E2-b%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2=%2820%2A25%2F%2820%2B25%29%5E2%29%28%2820%2B25%29%5E2-30%5E2%29+ ALIGN=MIDDLE  ALT=\"d%5E2=%2820%2A25%2F%2820%2B25%29%5E2%29%28%2820%2B25%29%5E2-30%5E2%29+\"   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=d%5E2=%28500%2F%2845%29%5E2%29%28%2845%29%5E2-30%5E2%29+ ALIGN=MIDDLE  ALT=\"d%5E2=%28500%2F%2845%29%5E2%29%28%2845%29%5E2-30%5E2%29+\"   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=d%5E2=%28500%2F%282025%29%29%282025-900%29+ ALIGN=MIDDLE  ALT=\"d%5E2=%28500%2F%282025%29%29%282025-900%29+\"   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=d%5E2=0.25%281125%29+ ALIGN=MIDDLE  ALT=\"d%5E2=0.25%281125%29+\"   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=d%5E2=281.25 ALIGN=MIDDLE  ALT=\"d%5E2=281.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=16.77 ALIGN=MIDDLE  ALT=\"d=16.77\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER\r<BR>\n" );
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document.write( "find the length of the line segment joining the midpoints of the 20-cm and 30-cm sides.\r<BR>\n" );
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document.write( "The mid-segment of a triangle (also called a midline) is a segment joining the midpoints of two sides of a triangle.\r<BR>\n" );
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document.write( "Properties:<BR>\n" );
document.write( "1.<BR>\n" );
document.write( "The mid-segment of a triangle joins the midpoints of two sides of a triangle such that it is parallel to the third side of the triangle.<BR>\n" );
document.write( "	<BR>\n" );
document.write( "2.<BR>\n" );
document.write( "The mid-segment of a triangle joins the midpoints of two sides of a triangle such that its length is half the length of the third side of the triangle.\r<BR>\n" );
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document.write( "so, the third side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25cm ALIGN=MIDDLE  ALT=\"25cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  the half of the third side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12.5cm ALIGN=MIDDLE  ALT=\"12.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ANSWER\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );