document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193627>Question 1193627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given:	<BR>\n" );
document.write( "△ABC with m∠A = 45°, m∠B = 30°, and<BR>\n" );
document.write( "BC = 14<BR>\n" );
document.write( "Find:	AB<BR>\n" );
document.write( "Draw altitude <BR>\n" );
document.write( "CD<BR>\n" );
document.write( " from C to <BR>\n" );
document.write( "AB.<BR>\n" );
document.write( " Determine the measures of ∠DCA and ∠DCB in degrees.<BR>\n" );
document.write( "m∠DCA	=	<BR>\n" );
document.write( " °<BR>\n" );
document.write( "m∠DCB	=	<BR>\n" );
document.write( " °<BR>\n" );
document.write( "Find the exact lengths of <BR>\n" );
document.write( "CD, AD, and DB.<BR>\n" );
document.write( "CD	=	<BR>\n" );
document.write( " <BR>\n" );
document.write( "AD	=	<BR>\n" );
document.write( " <BR>\n" );
document.write( "DB	=	<BR>\n" );
document.write( " <BR>\n" );
document.write( "Find AB. Give both an exact solution and an approximate solution to two decimal places.<BR>\n" );
document.write( "exact	AB	=	<BR>\n" );
document.write( " <BR>\n" );
document.write( "approximate	AB	=	<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825699 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Use the figure shown by one of the tutors to solve the problem without the complicated trigonometry and decimal approximations shown in the response from the other tutor.<br><BR>\n" );
document.write( "When altitude CD is drawn, triangle BCD is a 30-60-90 right triangle with hypotenuse BC=14; that makes CD=7 and BD=7*sqrt(3).<br><BR>\n" );
document.write( "And triangle ACD is a 45-45-90 right triangle with CD=7, so AD=7 also.<br><BR>\n" );
document.write( "And then AB = AD+DB = 7+7*sqrt(3).<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );