document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074041>Question 1074041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please answer this is really hard. The observed angles of a quadrilateral after station and side adjusmtments are: Angle DBA=30 Degrees angle CBD=48 Degrees angle BCA=59 Degrees and angle DCA =21 degrees. Compute the angles BDA,DAC and DAB </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688916 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=688916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not know what was meant by \"station and side adjustments.\"<BR>\n" );
document.write( "I imagine the quadrilateral (with its diagonals) looks like this,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C400%2C-1%2C11%2C-2%2C14%2C%0D%0Atriangle%280%2C0%2C10%2C0%2C1.638%2C9.287%29%2C%0D%0Atriangle%280%2C0%2C10%2C0%2C7.387%2C12.294%29%2C%0D%0Atriangle%287.387%2C12.294%2C1.638%2C9.287%2C4.002%2C6.661%29%2C%0D%0Alocate%28-0.1%2C0%2CC%29%2Clocate%289.9%2C0%2CB%29%2C%0D%0Alocate%281.5%2C10%2CD%29%2Clocate%287.3%2C12.9%2CA%29%2C%0D%0Alocate%283.9%2C6.5%2CX%29%2Cred%28arc%280%2C0%2C3%2C3%2C-59%2C0%29%29%2C%0D%0Alocate%280.4%2C0.9%2Cred%2859%5Eo%29%29%2C%0D%0Ared%28arc%280%2C0%2C3.6%2C3.6%2C-80%2C-59%29%29%2C%0D%0Alocate%280.5%2C2.7%2Cred%2821%5Eo%29%29%2C%0D%0Ared%28arc%2810%2C0%2C3.6%2C3.6%2C180%2C228%29%29%2C%0D%0Alocate%288.4%2C0.9%2Cred%2848%5Eo%29%29%2C%0D%0Ared%28arc%2810%2C0%2C4.2%2C4.2%2C228%2C258%29%29%2C%0D%0Alocate%288.5%2C2.7%2Cred%2830%5Eo%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > or a rotated and/or flipped version.<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DBA=30%5Eo ALIGN=MIDDLE  ALT=\"DBA=30%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CBD=48%5Eo ALIGN=MIDDLE  ALT=\"CBD=48%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCA=59%5Eo ALIGN=MIDDLE  ALT=\"BCA=59%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DCA+=21%5Eo ALIGN=MIDDLE  ALT=\"DCA+=21%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BCD=BCA%2BDCA=59%5Eo%2B21%5Eo=80%5Eo ALIGN=MIDDLE  ALT=\"BCD=BCA%2BDCA=59%5Eo%2B21%5Eo=80%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CBA=CBD%2BDBA=48%5Eo%2B30%5Eo=78%5Eo ALIGN=MIDDLE  ALT=\"CBA=CBD%2BDBA=48%5Eo%2B30%5Eo=78%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DXA=CXB=180%5Eo-59%5Eo-48%5Eo=73%5Eo ALIGN=MIDDLE  ALT=\"DXA=CXB=180%5Eo-59%5Eo-48%5Eo=73%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BAC=180%5Eo-59%5Eo-78%5Eo=43%5Eo ALIGN=MIDDLE  ALT=\"BAC=180%5Eo-59%5Eo-78%5Eo=43%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > based on the sum of angle measures for triangles BXC and BAC respectively.<BR>\n" );
document.write( " <BR>\n" );
document.write( "With that, I can compute approximate measures for BDA, DAC and DAB.<BR>\n" );
document.write( "It takes quite a bit of coordinate geometry calculations, and I do not get an exact value, but it is the best I can do so far.<BR>\n" );
document.write( "For ease of calculations, I set coordinates for points C and B as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%280%2C0%29 ALIGN=MIDDLE  ALT=\"C%280%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2810%2C0%29 ALIGN=MIDDLE  ALT=\"B%2810%2C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then I find coordinates for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%28x%5BD%5D%2Cy%5BD%5D%29 ALIGN=MIDDLE  ALT=\"D%28x%5BD%5D%2Cy%5BD%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28x%5BA%5D%2Cy%5BA%5D%29 ALIGN=MIDDLE  ALT=\"A%28x%5BA%5D%2Cy%5BA%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%5BD%5Dcot%2880%5Eo%29=x%5BD%5D%2Cy%5BD%5Dcot%2848%5Eo%29=10-x%5BD%5D%29 ALIGN=MIDDLE  ALT=\"system%28y%5BD%5Dcot%2880%5Eo%29=x%5BD%5D%2Cy%5BD%5Dcot%2848%5Eo%29=10-x%5BD%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%5BD%5Dcot%2880%5Eo%29=x%5BD%5D%2Cy%5BD%5D%28cot%2880%5Eo%29%2Bcot%2848%5Eo%29%29=10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y%5BD%5Dcot%2880%5Eo%29=x%5BD%5D%2Cy%5BD%5D=10%2F%28cot%2880%5Eo%29%2Bcot%2848%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5BD%5D=10cot%2880%5Eo%29%2F%28cot%2880%5Eo%29%2Bcot%2848%5Eo%29%29%2Cy%5BD%5D=10%2F%28cot%2880%5Eo%29%2Bcot%2848%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Approximate value: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%281.638%2C9.287%29 ALIGN=MIDDLE  ALT=\"D%281.638%2C9.287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Similarly for A,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5BA%5D=10cot%2859%5Eo%29%2F%28cot%2859%5Eo%29%2Bcot%2878%5Eo%29%29%2Cy%5BA%5D=10%2F%28cot%2859%5Eo%29%2Bcot%2878%5Eo%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Approximate value: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%287.387%2C12.294%29 ALIGN=MIDDLE  ALT=\"A%287.387%2C12.294%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(I have my computer keep more digits in these calculations, because they are intermediate calculations, and I round at the end).<BR>\n" );
document.write( "The slope of line DA is the tangent of the angle DA makes with the x-axis (or with any horizontal line).<BR>\n" );
document.write( "It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812.294-9.287%29%2F%287.387-1.638%29=3.006%2F5.749=0.5230 ALIGN=MIDDLE  ALT=\"%2812.294-9.287%29%2F%287.387-1.638%29=3.006%2F5.749=0.5230\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is the tangent of approximately a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27.6%5Eo ALIGN=MIDDLE  ALT=\"27.6%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle.<BR>\n" );
document.write( "Since line BD makes a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48%5Eo ALIGN=MIDDLE  ALT=\"-48%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > angle with the horizontal,<BR>\n" );
document.write( "the measure of angle BDA is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BDA=27.6%5Eo%2B48%5Eo=75.6%5Eo ALIGN=MIDDLE  ALT=\"BDA=27.6%5Eo%2B48%5Eo=75.6%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DAC=59%5Eo-27.6%5Eo=31.4%5Eo ALIGN=MIDDLE  ALT=\"DAC=59%5Eo-27.6%5Eo=31.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > based on the angles DA and AC make with the x-axis.<BR>\n" );
document.write( "Or, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DAC=180%5Eo-73%5Eo-27.6%5Eo=31.4%5Eo ALIGN=MIDDLE  ALT=\"DAC=180%5Eo-73%5Eo-27.6%5Eo=31.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > based on the sum of angle measures for triangle ADX.<BR>\n" );
document.write( "Finally, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DAB=DAC%2BBAC=31.4%5Eo%2B43%5Eo=74.4%5Eo ALIGN=MIDDLE  ALT=\"DAB=DAC%2BBAC=31.4%5Eo%2B43%5Eo=74.4%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );