document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198572>Question 1198572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two lighthouses are located on a north-south line. From lighthouse A, the bearing of a ship 3742 meters away is 129°43’. From lighthouse B, the bearing of the ship is 39°43’. Find the distance between the lighthouses. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832211 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = distance between the two lighthouses<BR>\n" );
document.write( "A & B = the two lighthouses<BR>\n" );
document.write( "C = location of the ship<BR>\n" );
document.write( "D = helper point to label the upper-most red angle<BR>\n" );
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document.write( "The diagram was made with GeoGebra.\r<BR>\n" );
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document.write( "The red angles are given. <BR>\n" );
document.write( "The blue angle is computed like this:<BR>\n" );
document.write( "(angle DAC)+(angle CAB) = 180<BR>\n" );
document.write( "angle CAB = 180 - (angle DAC)<BR>\n" );
document.write( "angle CAB = 180 - (129°43’)<BR>\n" );
document.write( "angle CAB = 179°60’ - (129°43’)<BR>\n" );
document.write( "angle CAB = (179°-129°)+(60’-43’)<BR>\n" );
document.write( "angle CAB = 50°17’\r<BR>\n" );
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document.write( "Then notice how<BR>\n" );
document.write( "(angle CAB)+(angle CBA) = (50°17’)+(39°43’)<BR>\n" );
document.write( "(angle CAB)+(angle CBA) = (50°+39°)+(17’+43’)<BR>\n" );
document.write( "(angle CAB)+(angle CBA) = 89°60’ <BR>\n" );
document.write( "(angle CAB)+(angle CBA) = 90°<BR>\n" );
document.write( "Which shows that triangle ABC is a right triangle. The 90 degree angle is located at point C.\r<BR>\n" );
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document.write( "This allows us to use the trig ratio sine to say<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(angle ABC) = AC/AB<BR>\n" );
document.write( "sin(39°43’) = 3742/x<BR>\n" );
document.write( "sin(39+43/60) = 3742/x<BR>\n" );
document.write( "sin(39.716667) = 3742/x\r<BR>\n" );
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document.write( "I'll let you finish up.<BR>\n" );
document.write( "Make sure your calculator is in degree mode.<BR>\n" );
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