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" );
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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 #825678 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a/sin A=c/sin C and angle C is 105deg. Side c is AB.<BR>\n" );
document.write( "14/sin45=x/sin 105<BR>\n" );
document.write( "x=14*sin 105/sin45<BR>\n" );
document.write( "=19.12<BR>\n" );
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document.write( "Altitudes are perpendicular so triangle ADC is a right triangle and angle DCA is 45 degrees and angle DCB is 60 degrees.<BR>\n" );
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document.write( "Get AC or side b as well: 14/sin 45=b/sin 30<BR>\n" );
document.write( "sin 30 is 0.5<BR>\n" );
document.write( "b=14 sin30/sin45=7/sqrt(2)/2 or 7 sqrt(2)=9.90, which is the hypotenuse.<BR>\n" );
document.write( "The legs are each hyp/sqrt(2) or 7 The altitude is 7<BR>\n" );
document.write( "That is also AD<BR>\n" );
document.write( "So DB is 12.12<BR>\n" );
document.write( "the right triangles are 7/7/9.9 and 12.12/7/14\r<BR>\n" );
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document.write( "AD=x and DB is 19.12-x<BR>\n" );
document.write( "ACD is a right triangle, so x^2+alt^2=7^2=49<BR>\n" );
document.write( "(19-x)^2+49=196<BR>\n" );
document.write( "(19-x)^2=147<BR>\n" );
document.write( "19-x=12.12 AB approx<BR>\n" );
document.write( "the exact value is sqrt(147)AB exact\r<BR>\n" );
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