document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135183>Question 1135183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship is anchored off a long straight shoreline that runs north and south. From two observation points 19 miles apart on shore, the bearings of the ship are N 36° E and S 56° E. What is the shortest distance from the ship to the shore? (Round your answer to the nearest tenth.)<BR>\n" );
document.write( " <BR>\n" );
document.write( "=             mi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752838 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=752838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ship and the two shore points form a triangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A is the north point on the shore.<BR>\n" );
document.write( "B is the ship.<BR>\n" );
document.write( "C is the south point on the shore.<BR>\n" );
document.write( "angle A is 56 degrees.<BR>\n" );
document.write( "angle C is 36 degrees.<BR>\n" );
document.write( "draw a line from point B perpendicular to the line AC and connecting to line AC at point D.<BR>\n" );
document.write( "line BD is the shortest distance to the shore.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the length of the line AC is 19.<BR>\n" );
document.write( "let the length of the line AD be equal to x and the length of the line DC be equal to 19 - x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let the length of the line BD be equal to h .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "two right triangles are formed with a common line of BD.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these are two right triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "tan(56) = h / x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "tan(36) = h / (19 - x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for h in both equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "h = x * tan(56).<BR>\n" );
document.write( "h = (19 - x) * tan(36).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since they're both equal to h, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x * tan(56) = (19 - x) * tan(36)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get x * tan(56) = 19 * tan(36) - x * tan(36).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add x * tan(36) to both sides of this equation to get x * tan(56) + x * tan(36) = 19 * tan(36).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor out the x to get x * (tan(56) + tan(36)) = 19 * tan(36).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by (tan(56) + tan(36)) to get x = 19 * tan(36) / (tan(56) + tan(36)).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 6.248828112.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes 19 - x equal to 12.75117189.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in triangle ABD, you get tan(56) = h / x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for h to get h = x * tan(56) which becomes h = 6.248828112 * tan(56) which makes h = 9.264268658.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in triangle CBD, you get tan(36) = h / (19 - x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for h to get h = (19 - x) * tan(36) which becomes h = 12.75117189 * tan(36) which makes h = 9.264268658.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirms that h = 9.264268658 miles which is the shortest distance to land.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's my diagram of the situation as i see it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/022101.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );