document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43163>Question 43163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two surveyors are on the opposite sides of a swamp. To find the distance between them, one surveyor locates a point T that is 180 m to point P, her location. The other surveyor locates point R, which is 80 m from point T and creates an angle of 72o for angle PTR. Find the distance across the swamp (PR). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28256 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is very if you draw the figure first.<BR>\n" );
document.write( "Consider the triangle PTR.<BR>\n" );
document.write( "Let p, t and r be the lengths of the sides RT, PR and PT respectively. <BR>\n" );
document.write( "Also, denote the internal abgles of the triangle as P, T and R e.g. < RTP = T.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-100%2C100%2C-10%2C90%2C%0D%0Aline%28-90%2C0%2C90%2C0%29%2C%0D%0Aline%2890%2C0%2C-65.28%2C76.084%29%2C%0D%0Aline%28-65.28%2C76.084%2C-90%2C0%29%2C%0D%0Alocate%28-93%2C0%2CT%29%2C%0D%0Alocate%2893%2C0%2CP%29%2C%0D%0Alocate%28-66%2C85%2CR%29%2C%0D%0Alocate%280%2C-2%2Cr=180%29%2C%0D%0Alocate%2830%2C38%2Ct=unknown%29%2C%0D%0Alocate%28-75%2C40%2Cp=80%29%2C%0D%0Alocate%28-86%2C15%2C72%5Eo%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Look, you know from the given data that r = 180 m, p = 80 m and T = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%5Eo ALIGN=MIDDLE  ALT=\"72%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Now you are required to find 't'.<BR>\n" );
document.write( "In order to find 't' apply cosine rule.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+p%5E2+%2B+r%5E2+-+2%2Ap%2Ar%2Acos%28T%29 ALIGN=MIDDLE  ALT=\"t%5E2+=+p%5E2+%2B+r%5E2+-+2%2Ap%2Ar%2Acos%28T%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+80%5E2+%2B+180%5E2+-+2%2A80%2A180%2Acos%2872%5Eo%29 ALIGN=MIDDLE  ALT=\"t%5E2+=+80%5E2+%2B+180%5E2+-+2%2A80%2A180%2Acos%2872%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+6400+%2B+32400+-+28800cos%2872%5Eo%29 ALIGN=MIDDLE  ALT=\"t%5E2+=+6400+%2B+32400+-+28800cos%2872%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+38800+-+28800%2A0.309 ALIGN=MIDDLE  ALT=\"t%5E2+=+38800+-+28800%2A0.309\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+38800+-+8899.7 ALIGN=MIDDLE  ALT=\"t%5E2+=+38800+-+8899.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+29900.3 ALIGN=MIDDLE  ALT=\"t%5E2+=+29900.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+sqrt%2829900.3%29 ALIGN=MIDDLE  ALT=\"t+=+sqrt%2829900.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+172.92 ALIGN=MIDDLE  ALT=\"t+=+172.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence, the required length of PR is 172.92 m. </SPAN>\n" );
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