document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122327>Question 1122327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ship S is sighted from two lighthouses B and U which are 16 km apart. If m&#8736;SBU= 27° and m&#8736;SUB= 65°. Find the distance from S to the nearer lighthouse.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738418 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=738418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this forms triangle SBU where angle SBU = 27 degrees and angle SUB = 65 degrees.\r<BR>\n" );
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document.write( "angle BSU is equal to 180 - 27 - 65 = 88 degrees.\r<BR>\n" );
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document.write( "88 + 27 + 65 = 180, as it should, since the sum of the interior angles of a triangle is 180 degrees.\r<BR>\n" );
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document.write( "BU = 16 kilometers.\r<BR>\n" );
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document.write( "use the law of sines to find the length of sides BS and SU.\r<BR>\n" );
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document.write( "law of sines says:   a/sin(A) = b/sin(B) = c/sin(C)\r<BR>\n" );
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document.write( "applied to this triangle, you get 16/sin(88) = SU/sin(27) = SB/sin(65)\r<BR>\n" );
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document.write( "this can be broken up into:\r<BR>\n" );
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document.write( "16/sin(88) = SU/sin(27) and 16/sin(88) = SB/sin(65)\r<BR>\n" );
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document.write( "cross multiply each to get:\r<BR>\n" );
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document.write( "16 * sin(27) = sin(88) * SU and 16 * sin(65) = SB * sin(88)\r<BR>\n" );
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document.write( "solve for SU to get SU = 16 * sin(27) / sin(88) = 7.298275633\r<BR>\n" );
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document.write( "solve for SB to get SB = 16 * sin(65) / sin(88) = 14.50976355\r<BR>\n" );
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document.write( "the distance from S to the nearer lighthouse is 7.298275633 kilometers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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