document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111722>Question 1111722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship is approaching a harbour between a pier and a lighthouse. The distance between the pier and the lighthouse is 4.1 nautical miles. The angle between the lines of sight from the ship to the pier and the lighthouse is 120°. The lighthouse keeper reports that the ship is 3.5 nautical miles away. Determine the distance between the ship and the pier, to two decimal places.\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726765 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A ship is approaching a harbour between a pier and a lighthouse.<BR>\n" );
document.write( " The distance between the pier and the lighthouse is 4.1 nautical miles.<BR>\n" );
document.write( " The angle between the lines of sight from the ship to the pier and the lighthouse is 120°.<BR>\n" );
document.write( " The lighthouse keeper reports that the ship is 3.5 nautical miles away.<BR>\n" );
document.write( " Determine the distance between the ship and the pier, to two decimal places.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Draw this out as a triangle, the pier, the lighthouse and the boat<BR>\n" );
document.write( "angle at the boat is 120 degrees, side opposite is 4.1 mi<BR>\n" );
document.write( "side opposite the lighthouse is the distance from the boat to the pier<BR>\n" );
document.write( "Find the angle P at the pier using the law of sines<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5%2Fsin%28P%29 ALIGN=MIDDLE  ALT=\"3.5%2Fsin%28P%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.1%2Fsin%28120%29 ALIGN=MIDDLE  ALT=\"4.1%2Fsin%28120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "4.1*sin(P) = 3.5*sin(120)<BR>\n" );
document.write( "sin(P) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.031%2F4.1 ALIGN=MIDDLE  ALT=\"3.031%2F4.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = 47.67 degrees<BR>\n" );
document.write( "Find the angle at the lighthouse<BR>\n" );
document.write( "180 - 120 - 47.67 = 12.331 degrees<BR>\n" );
document.write( "Side opposite is the dist between the boat and the pier<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2Fsin%2812.331%29 ALIGN=MIDDLE  ALT=\"d%2Fsin%2812.331%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.1%2Fsin%28120%29 ALIGN=MIDDLE  ALT=\"4.1%2Fsin%28120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = .3156*4.734<BR>\n" );
document.write( "d = 1.01 mile from the boat to the pier<BR>\n" );
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