document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189731>Question 1189731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> While standing on a 75m tall bridge, given can see two boats. From his position on the bridge, the first boat is located on a bearing of 70 degrees and the second boat is located on a bearing of 300 degrees. Gavin estimates that the angles of depression for each of the boats are 38 degrees and 47 degrees respectively. How far apart are the boats?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821198 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> While standing on a 75m tall bridge, given can see two boats.<BR>\n" );
document.write( " From his position on the bridge, the first boat is located on a bearing of 70 degrees and the second boat is located on a bearing of 300 degrees.<BR>\n" );
document.write( " Gavin estimates that the angles of depression for each of the boats are 38 degrees and 47 degrees respectively.<BR>\n" );
document.write( " How far apart are the boats?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "find the actual distance from the observer to each boat.<BR>\n" );
document.write( "a right angle is formed from the water, 75' below the bridge. to the boat.<BR>\n" );
document.write( "the distance to boat will be the hypotenuse (h). <BR>\n" );
document.write( "Find the interior angle from the given depression, 90-47 = 43 degrees<BR>\n" );
document.write( "Cos(43) = 75/h<BR>\n" );
document.write( "h = 102.55 m to one boat<BR>\n" );
document.write( "find the distance to the other boat interior angle = 90-38 = 52 degrees<BR>\n" );
document.write( "cos(52) = 75/h<BR>\n" );
document.write( "h = 121.82 m to the other boat<BR>\n" );
document.write( ":<BR>\n" );
document.write( "these form the two sides of a triangle from the observer to each boat, the angle at the observer: 300=70 = 230 degrees (A), distance between the boats is a<BR>\n" );
document.write( "Use the law of cosines to find a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+b%5E2+%2B+c%5E2+-+%282bc%29%2ACos%28A%29 ALIGN=MIDDLE  ALT=\"a%5E2+=+b%5E2+%2B+c%5E2+-+%282bc%29%2ACos%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+102.55%5E2+%2B+121.82%5E2+-2%28102.55%2A121.82%29+%2A+Cos%28230%29 ALIGN=MIDDLE  ALT=\"a%5E2+=+102.55%5E2+%2B+121.82%5E2+-2%28102.55%2A121.82%29+%2A+Cos%28230%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You do this tedious math yourself, I got<BR>\n" );
document.write( "a = 203.5 m between the boats\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );