document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121074>Question 1121074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two Coast Guard stations, A and B, are on an east-west line and are 110 km apart.   The bearing of a ship from station A is S 56o E, and the bearing of the same ship from station B is S 38o W.\r<BR>\n" );
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document.write( "a)   How far is the ship from the east-west line connecting the two Coast Guard stations.<BR>\n" );
document.write( "b)   How far is the ship from station A?<BR>\n" );
document.write( "c)   How far is the ship from station B?    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736834 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=736834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can draw triangle ABC as shown in the diagram below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/080901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "line segment AB of this triangle is equal to a distance of 110 kilometers.<BR>\n" );
document.write( "point A of this triangle is one of the stations.<BR>\n" );
document.write( "point B of this triangle is the other one of the stations.<BR>\n" );
document.write( "point C of this triangle is the location of the ship.\r<BR>\n" );
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document.write( "the ship is 56 degrees south east of point A and 38 degrees south west of point B, as shown in the diagram.\r<BR>\n" );
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document.write( "line segment AB in the diagram is a horizontal line because it is on the east-west line of the diagram.\r<BR>\n" );
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document.write( "the vertical lines emnating from point A and B form a 90 degree with the horizontal line.\r<BR>\n" );
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document.write( "angle A of triangle ABC is therefore equal to 90 - 56 = 34 degrees.<BR>\n" );
document.write( "angle B of triangle ABC is therefore equal to 90 - 38 = 52 degrees.\r<BR>\n" );
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document.write( "since the sum of the angles of a triangle is 180 degrees, that makes angle C equal to 94 degrees.\r<BR>\n" );
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document.write( "110 kilometers is opposite angle C of this triangle.<BR>\n" );
document.write( "line segment b is opposite angle B of this triangle.<BR>\n" );
document.write( "line segment a is opposite angle A of this triangle.\r<BR>\n" );
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document.write( "by the law of sines, 110 / sin(C) = a / sin(A) = b / sin(B)\r<BR>\n" );
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document.write( "to find a, you would take 110 / sin(C) = a / sin(A)\r<BR>\n" );
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document.write( "to find b, you would take 110 / sin(C) = b / sin(B)\r<BR>\n" );
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document.write( "solve for a to get a = 110 * sin(A) / sin(C)\r<BR>\n" );
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document.write( "solve for b to get b = 110 * sin(B) / sin(C)\r<BR>\n" );
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document.write( "these equations become:\r<BR>\n" );
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document.write( "a = 110 * sin(34) / sin(94) = 61.66142351 kilometers.\r<BR>\n" );
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document.write( "b = 110 * ain(52) / ain(94) = 86.89284951 kilometers.\r<BR>\n" );
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document.write( "b is the distance of the ship from location A.\r<BR>\n" );
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document.write( "a is the distance of the ship from location B.\r<BR>\n" );
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document.write( "a is equal to line segment BC in the diagram.\r<BR>\n" );
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document.write( "b is equal to line segment AC in the diagram.\r<BR>\n" );
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document.write( "note that a = 110 * sin(34) / sin(94) is the same as BC = 110 * sin(34) / sin(94) as shown in the diagram.\r<BR>\n" );
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document.write( "in other words, a and line segment BC are one and the same line segment.\r<BR>\n" );
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document.write( "note also that b = 110 * ain(52) / ain(94) is the same as AC = 110 * sin(52) / sin(94) as shown in the diagram.\r<BR>\n" );
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document.write( "in other words, b and line segment AC are one and the same line segment.\r<BR>\n" );
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document.write( "your solution is that the distance of the ship from point A is 86.89284951 kilometers and the distance of the ship from point B is 61.66142351 kilometers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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