document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121308>Question 1121308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two coast guard stations, A and B are on an east-west line and are 76 km apart.   The bearing of a ship from station A is N 49o E and the bearing of the same ship from station B is N 61o W.   If the ship gets an emergency call that a capsized vessel is somewhere between the two coast guard stations and the ship, find the area of ocean that the ship must search to find the capsized vessel. \r<BR>\n" );
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document.write( "Round your answer to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737143 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737143\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Since the ship bears N49°E of A, angle A of the triangle must be 41°.  Likewise, based on the bearing of the ship from B, angle B of the triangle must be 29°.  Then, because the sum of the angles in any triangle is 180°, the third angle of the triangle must be 110°.\r<BR>\n" );
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document.write( "Use the Law of Sines to calculate the distance from A to the Ship, hereafter <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sin\,110^\circ}{76}\ =\ \frac{\sin\,29^\circ}{x}\">\r<BR>\n" );
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document.write( "Construct the NS line through the Ship to create a right triangle where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is the hypotenuse and angle A is one of the acute angles.\r<BR>\n" );
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document.write( "Then the distance from the ship to the EW line that we will call <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> is the height of triangle ASB.  Calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\"> by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h\ =\ x\sin(41^\circ)\">\r<BR>\n" );
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document.write( "Once you have calculated <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">, calculate the desired area by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ \frac{76h}{2}\text{ km^2}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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