document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=453480>Question 453480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In Triangle ABC, A= 42 degrees, B= 68 degrees, and c= 15. Find the length of a and b<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 #311573 by </B><A HREF=/tutors/aboutme.mpl?userid=pedjajov><B>pedjajov(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pedjajov><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=311573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we draw a height h from vertex C it divides side c in point D into two pieces x=AD and y=BD<BR>\n" );
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document.write( "Also it forms two right triangles:<BR>\n" );
document.write( "- triangle ADC with one leg being height other one being x and b for hypotenuse<BR>\n" );
document.write( "- triangle BDC with one leg being height other one being y and a for hypotenuse<BR>\n" );
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document.write( "We have for x, y and c:<BR>\n" );
document.write( "x+y=c -> x+y=15 -> x=15-y<BR>\n" );
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document.write( "In triangle ADC we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2842%29=h%2Fx ALIGN=MIDDLE  ALT=\"tan%2842%29=h%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=x%2Atan%2842%29 ALIGN=MIDDLE  ALT=\"h=x%2Atan%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In triangle BDC we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2868%29=h%2Fy ALIGN=MIDDLE  ALT=\"tan%2868%29=h%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=y%2Atan%2868%29 ALIGN=MIDDLE  ALT=\"h=y%2Atan%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we have -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Atan%2842%29=y%2Atan%2868%29 ALIGN=MIDDLE  ALT=\"x%2Atan%2842%29=y%2Atan%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If we substitute x with x=15-y we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815-y%29%2Atan%2842%29=y%2Atan%2868%29 ALIGN=MIDDLE  ALT=\"%2815-y%29%2Atan%2842%29=y%2Atan%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Atan%2842%29-y%2Atan%2842%29=y%2Atan%2868%29 ALIGN=MIDDLE  ALT=\"15%2Atan%2842%29-y%2Atan%2842%29=y%2Atan%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Atan%2842%29=y%2Atan%2842%29%2By%2Atan%2868%29 ALIGN=MIDDLE  ALT=\"15%2Atan%2842%29=y%2Atan%2842%29%2By%2Atan%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=15%2Atan%2842%29%2F%28tan%2842%29%2Btan%2868%29%29 ALIGN=MIDDLE  ALT=\"y=15%2Atan%2842%29%2F%28tan%2842%29%2Btan%2868%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "From here:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15-y ALIGN=MIDDLE  ALT=\"x=15-y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=15%2Atan%2868%29%2F%28tan%2842%29%2Btan%2868%29%29 ALIGN=MIDDLE  ALT=\"x=15%2Atan%2868%29%2F%28tan%2842%29%2Btan%2868%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Knowing x we can find b=AC:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2842%29=x%2Fb ALIGN=MIDDLE  ALT=\"cos%2842%29=x%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=x%2Fcos%2842%29 ALIGN=MIDDLE  ALT=\"b=x%2Fcos%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15%2Atan%2868%29%2Fcos%2842%29%28tan%2842%29%2Btan%2868%29%29 ALIGN=MIDDLE  ALT=\"b=15%2Atan%2868%29%2Fcos%2842%29%28tan%2842%29%2Btan%2868%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "b=14.80<BR>\n" );
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document.write( "Knowing y we can find c=BC:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%2868%29=y%2Fc ALIGN=MIDDLE  ALT=\"cos%2868%29=y%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=y%2Fcos%2868%29 ALIGN=MIDDLE  ALT=\"c=y%2Fcos%2868%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=15%2Atan%2842%29%2Fcos%2868%29%28tan%2842%29%2Btan%2868%29%29 ALIGN=MIDDLE  ALT=\"c=15%2Atan%2842%29%2Fcos%2868%29%28tan%2842%29%2Btan%2868%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "c=10.68 </SPAN>\n" );
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