document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207648>Question 1207648</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you please help me solve this problem? Thank you.<BR>\n" );
document.write( "A surveyor wishes to find the distance between two inaccessible points A and B. As shown in the figure, two points C and D are selected from which it is possible to view both A and B. The distance CD and the angles ACD, ACB, BDC, and BDA are then measured. If CD=120~ft, ∠ACD=115°, ∠ACB=92°, ∠BDC=125°, and ∠BDA=100°, approximate the distance AB. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845633 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=845633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to the diagram tutor Edwin has drawn.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28405%2C1568%2F9%2C-40%2C185%2C-10%2C88%2C%0D%0A%0D%0Atriangle%28-30.82762166%2C66.110048%2C120%2C0%2C0%2C0%29%2C%0D%0Atriangle%280%2C0%2C120%2C0%2C174.8922588%2C78.39426942%29%2C%0D%0Atriangle%28-30.82762166%2C66.110048%2C174.8922588%2C78.39426942%2C174.8922588%2C78.39426942%29%2C%0D%0A%0D%0Alocate%280%2C0%2CC%29%2C+locate%28120%2C0%2CD%29%2C%0D%0Alocate%28-31%2C75%2CA%29%2Clocate%28175%2C87%2CB%29%2C+locate%2850%2C0%2Cmatrix%281%2C2%2C120%2Cft%29%29%2C%0D%0A%0D%0Alocate%2857%2C36%2CE%29%2C%0D%0A%0D%0A%0D%0Ared%28arc%280%2C0%2C50%2C-50%2C0%2C115%29%2Clocate%287%2C35%2C115%5Eo%29%29%2Cblue%28arc%280%2C0%2C39%2C-39%2C23%2C115%29%2Clocate%28-2.7%2C17%2C92%5Eo%29%29%2C%0D%0A%0D%0Ared%28arc%28120%2C0%2C50%2C-50%2C55%2C180%29%2Clocate%28110%2C38%2C125%5Eo%29%29%2Cblue%28arc%28120%2C0%2C39%2C-39%2C55%2C155%29%2Clocate%28108%2C19%2C100%5Eo%29%29%2C%0D%0A%0D%0Agreen%28arc%280%2C0%2C60%2C-60%2C0%2C23%29%2Clocate%2830%2C16%2C23%5Eo%29%2C%0D%0Aarc%28120%2C0%2C60%2C-60%2C155%2C180%29%2Clocate%2877%2C13%2C25%5Eo%29%0D%0A%0D%0A%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are a lot of triangles to keep track of, so it might be helpful to peel the triangles ACD and BCD apart to get this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28605%2C1568%2F9%2C-40%2C345%2C-10%2C88%2C%0D%0A%0D%0Atriangle%28-30.82762166%2C66.110048%2C120%2C0%2C0%2C0%29%2C%0D%0Atriangle%280%2B150%2C0%2C120%2B150%2C0%2C174.8922588%2B150%2C78.39426942%29%2C%0D%0A%0D%0A%0D%0Alocate%280%2C0%2CC%29%2Clocate%280%2B150%2C0%2CC%29%2C+locate%28120%2C0%2CD%29%2Clocate%28120%2B150%2C0%2CD%29%2C%0D%0Alocate%28-31%2C75%2CA%29%2Clocate%28175%2B150%2C87%2CB%29%2C+locate%2850%2C0%2Cmatrix%281%2C2%2C120%2Cft%29%29%2Clocate%2850%2B150%2C0%2Cmatrix%281%2C2%2C120%2Cft%29%29%2C%0D%0A%0D%0A%0D%0Alocate%287%2C35-20%2C115%5Eo%29%2C%0D%0A%0D%0Alocate%28110%2B140%2C38-20%2C125%5Eo%29%2C%0D%0A%0D%0Alocate%2830%2B150%2C16%2C23%5Eo%29%2C%0D%0Alocate%2877%2C13%2C25%5Eo%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagrams aren't to scale.\r<BR>\n" );
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document.write( "Recall that for any triangle, the interior angles always add to 180 degrees.<BR>\n" );
document.write( "We'll use this fact to find the missing angles of triangles ACD and BCD.\r<BR>\n" );
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document.write( "For triangle ACD, the missing angle is A = 180-C-D = 180-115-25 = 40 degrees.<BR>\n" );
document.write( "For triangle BCD, the missing angle is B = 180-C-D = 180-23-125 = 32 degrees.\r<BR>\n" );
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document.write( "Let's update the diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28605%2C1568%2F9%2C-40%2C345%2C-10%2C88%2C%0D%0A%0D%0Atriangle%28-30.82762166%2C66.110048%2C120%2C0%2C0%2C0%29%2C%0D%0Atriangle%280%2B150%2C0%2C120%2B150%2C0%2C174.8922588%2B150%2C78.39426942%29%2C%0D%0A%0D%0A%0D%0Alocate%280%2C0%2CC%29%2Clocate%280%2B150%2C0%2CC%29%2C+locate%28120%2C0%2CD%29%2Clocate%28120%2B150%2C0%2CD%29%2C%0D%0Alocate%28-31%2C75%2CA%29%2Clocate%28175%2B150%2C87%2CB%29%2C+locate%2850%2C0%2Cmatrix%281%2C2%2C120%2Cft%29%29%2Clocate%2850%2B150%2C0%2Cmatrix%281%2C2%2C120%2Cft%29%29%2C%0D%0A%0D%0A%0D%0Alocate%287%2C35-20%2C115%5Eo%29%2C%0D%0A%0D%0Alocate%28110%2B140%2C38-20%2C125%5Eo%29%2C%0D%0A%0D%0Alocate%2830%2B150%2C16%2C23%5Eo%29%2C%0D%0Alocate%2877%2C13%2C25%5Eo%29%2C%0D%0A%0D%0A%0D%0Alocate%287-25%2C35%2B20%2C40%5Eo%29%2C%0D%0Alocate%287%2B280%2C35%2B30%2C32%5Eo%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From here, we have a few pathways we could take. <BR>\n" );
document.write( "The path I'll take is to determine the side AC (from triangle ACD) and determine side BC (from triangle BCD). <BR>\n" );
document.write( "Use the Law of Sines to find these lengths.\r<BR>\n" );
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document.write( "I'll get you started with the setup equations<BR>\n" );
document.write( "AC/sin(D) = CD/sin(A)<BR>\n" );
document.write( "AC/sin(25) = 120/sin(40)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "BC/sin(D) = CD/sin(B)<BR>\n" );
document.write( "BC/sin(125) = 120/sin(32)<BR>\n" );
document.write( "Make sure that your calculator is set to degrees mode.\r<BR>\n" );
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document.write( "I'll let the student finish this subsection.\r<BR>\n" );
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document.write( "Let's focus on triangle ABC.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28405%2C1568%2F9%2C-40%2C185%2C-10%2C88%2C%0D%0Atriangle%28-30.82762166%2C66.110048%2C174.8922588%2C78.39426942%2C0%2C0%29%2C%0D%0A%0D%0Alocate%280%2C0%2CC%29%2C%0D%0Alocate%28-31%2C75%2CA%29%2Clocate%28175%2C87%2CB%29%2C%0D%0A%0D%0Alocate%28-2.7%2C17%2C92%5Eo%29%0D%0A%0D%0A%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "The last batch of steps would be to use the Law of Cosines to find the length of side AB.<BR>\n" );
document.write( "x = length of AC<BR>\n" );
document.write( "y = length of BC<BR>\n" );
document.write( "z = length of AB\r<BR>\n" );
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document.write( "Law of Cosines<BR>\n" );
document.write( "z^2 = x^2 + y^2 - 2*x*y*cos(C)<BR>\n" );
document.write( "z^2 = x^2 + y^2 - 2*x*y*cos(92)\r<BR>\n" );
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document.write( "I'll let the student finish up.<BR>\n" );
document.write( "</font> </SPAN>\n" );
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