document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=855017>Question 855017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You are given the information that triangle ABC has an altitude of CD. Then you have to write a paragraph proof stating that the Sin A/a = Sin B/b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515056 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=515056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If angles A and B are acute, altitude CD divides the triangle, into two right triangles:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C3%2C-1.5%2C6.5%2C%0D%0Agreen%28rectangle%280%2C0%2C0.3%2C0.3%29%29%2C%0D%0Atriangle%28-4%2C0%2C2%2C0%2C0%2C5%29%2C%0D%0Agreen%28line%280%2C0%2C0%2C5%29%29%2C%0D%0Alocate%28-4.2%2C-0.1%2CA%29%2Clocate%282%2C-0.1%2CB%29%2C%0D%0Alocate%28-0.1%2C-0.1%2CD%29%2Clocate%28-0.1%2C5.5%2CC%29%2C%0D%0Alocate%28-2%2C2.5%2Cb%29%2Clocate%280.8%2C2.5%2Ca%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "In those right triangles, the trigonometric ratios involving altitude CD and angles A and B are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=CD%2Fb ALIGN=MIDDLE  ALT=\"sin%28A%29=CD%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=b%2Asin%28A%29 ALIGN=MIDDLE  ALT=\"CD=b%2Asin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29=CD%2Fa ALIGN=MIDDLE  ALT=\"sin%28B%29=CD%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=a%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"CD=a%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If one of the angles A and B is obtuse, sides AC and BC, along with altitude CD, and the line containing AB form two right triangles:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C3%2C-1.5%2C6.5%2C%0D%0Agreen%28rectangle%282%2C0%2C1.7%2C0.3%29%29%2C%0D%0Atriangle%28-4%2C0%2C0%2C0%2C2%2C5%29%2C%0D%0Agreen%28line%282%2C0%2C2%2C5%29%29%2Cgreen%28arrow%280%2C0%2C3%2C0%29%29%2C%0D%0Alocate%28-4.2%2C-0.1%2CA%29%2Clocate%282%2C-0.1%2CD%29%2C%0D%0Alocate%28-0.1%2C-0.1%2CB%29%2Clocate%281.9%2C5.5%2CC%29%2C%0D%0Alocate%28-1%2C2.5%2Cb%29%2Clocate%280.6%2C2.5%2Ca%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Ray BD is the extension of AB. Obtuse angle ABC is called angle B for short.<BR>\n" );
document.write( "Angle B and angle CBD are supplementary and therefore have the same sine.<BR>\n" );
document.write( "In right triangles ADC and BDC, the trigonometric ratios involving altitude CD and angles A and B are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=CD%2Fb ALIGN=MIDDLE  ALT=\"sin%28A%29=CD%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=b%2Asin%28A%29 ALIGN=MIDDLE  ALT=\"CD=b%2Asin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28B%29=sin%28CBD%29=CD%2Fa ALIGN=MIDDLE  ALT=\"sin%28B%29=sin%28CBD%29=CD%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=a%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"CD=a%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "In either case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=b%2Asin%28A%29 ALIGN=MIDDLE  ALT=\"CD=b%2Asin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=a%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"CD=a%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Asin%28A%29=a%2Asin%28B%29 ALIGN=MIDDLE  ALT=\"b%2Asin%28A%29=a%2Asin%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides of the equal sign by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab ALIGN=MIDDLE  ALT=\"ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28a%29%2Fa=sin%28B%29%2Fb ALIGN=MIDDLE  ALT=\"sin%28a%29%2Fa=sin%28B%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );