document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43248>Question 43248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, c = 10 and angle A = angle B = 40o. Find the length of the median to line segment AC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28280 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, BD is the median which bisects the side AC. <BR>\n" );
document.write( "Drop a perpendicular from C on AB intersecting AB at E.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-10%2C10%2C-2%2C8%2C%0D%0Aline%28-5%2C0%2C5%2C0%29%2C%0D%0Aline%28-5%2C0%2C0%2C4.196%29%2C%0D%0Aline%280%2C4.196%2C5%2C0%29%2C%0D%0Aline%285%2C0%2C-2.5%2C2.098%29%2C%0D%0Aline%280%2C4.196%2C0%2C0%29%2C%0D%0Alocate%285.5%2C0%2CB%29%2C%0D%0Alocate%28-5.5%2C0%2CA%29%2C%0D%0Alocate%280%2C5%2CC%29%2C%0D%0Alocate%28-3.5%2C3%2CD%29%2C%0D%0Alocate%280%2C-0.5%2CE%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In triangle ABC, < CAB = < CBA = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%5Eo ALIGN=MIDDLE  ALT=\"40%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and AB = 10 units.<BR>\n" );
document.write( "As triangle ABC is isoscles, so the perpendicular dropped from the vertex on the opposite bisects the opposite side.<BR>\n" );
document.write( "Hence, AE = BE = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2F2 ALIGN=MIDDLE  ALT=\"AB%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F2 ALIGN=MIDDLE  ALT=\"10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 units.\r<BR>\n" );
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document.write( "Now, in triangle AEC, < AEC is right angle.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AE%2FAC ALIGN=MIDDLE  ALT=\"AE%2FAC\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cos(< CAE)<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2FAC+=+cos%2840%5Eo%29 ALIGN=MIDDLE  ALT=\"5%2FAC+=+cos%2840%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+5%2Fcos%2840%5Eo%29 ALIGN=MIDDLE  ALT=\"AC+=+5%2Fcos%2840%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+5%2F0.839 ALIGN=MIDDLE  ALT=\"AC+=+5%2F0.839\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+6.527 ALIGN=MIDDLE  ALT=\"AC+=+6.527\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, AD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >AC = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.527%2F2 ALIGN=MIDDLE  ALT=\"6.527%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.263 units.\r<BR>\n" );
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document.write( "Now, consider triangle ADB.<BR>\n" );
document.write( "Apply cosine formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%5E2+=+AD%5E2+%2B+AB%5E2+-+2%2AAD%2AAB ALIGN=MIDDLE  ALT=\"BD%5E2+=+AD%5E2+%2B+AB%5E2+-+2%2AAD%2AAB\"   DISABLED_style= \"max-width:90%; height:auto;\" >cos(< BAD)<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%5E2+=+3.263%5E2+%2B+10%5E2+-+2%2A3.263%2A10%2Acos%2840%5Eo%29 ALIGN=MIDDLE  ALT=\"BD%5E2+=+3.263%5E2+%2B+10%5E2+-+2%2A3.263%2A10%2Acos%2840%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD%5E2+=+60.655 ALIGN=MIDDLE  ALT=\"BD%5E2+=+60.655\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD+=+sqrt%2860.655%29 ALIGN=MIDDLE  ALT=\"BD+=+sqrt%2860.655%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or BD = 7.788 units\r<BR>\n" );
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document.write( "Thus, the length of the median to the line segment AC is 7.788 units. </SPAN>\n" );
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