document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168437>Question 1168437</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ship travels on a N 28o E course.   The ship travels until it is due north of a port which is 200 nm due east of the port from which the ship originated.<BR>\n" );
document.write( "How far did the ship travel?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851569 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
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document.write( "**1. Visualize the Situation**\r<BR>\n" );
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document.write( "* Draw a horizontal line representing the east-west direction.<BR>\n" );
document.write( "* Let P1 be the port from which the ship originated.<BR>\n" );
document.write( "* Let P2 be the port due north of P1's final position.<BR>\n" );
document.write( "* P2 is 200 nautical miles (nm) east of P1.<BR>\n" );
document.write( "* The ship travels on a N 28° E course. This means it travels at an angle of 28° from the north direction towards the east.\r<BR>\n" );
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document.write( "**2. Set Up the Triangle**\r<BR>\n" );
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document.write( "* The ship travels from P1 to a point S.<BR>\n" );
document.write( "* S is due north of P2.<BR>\n" );
document.write( "* We have a right triangle P1SP2.<BR>\n" );
document.write( "* P1P2 = 200 nm (eastward distance)<BR>\n" );
document.write( "* Angle SP1P2 = 90° - 28° = 62°\r<BR>\n" );
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document.write( "**3. Use Trigonometry**\r<BR>\n" );
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document.write( "We need to find the distance P1S, which is the distance the ship traveled.\r<BR>\n" );
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document.write( "* We have angle SP1P2 = 62°, and we know the adjacent side (P1P2 = 200 nm).<BR>\n" );
document.write( "* We need to find the hypotenuse (P1S).<BR>\n" );
document.write( "* We can use the cosine function:\r<BR>\n" );
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document.write( "cos(angle) = adjacent / hypotenuse\r<BR>\n" );
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document.write( "* cos(62°) = P1P2 / P1S<BR>\n" );
document.write( "* cos(62°) = 200 / P1S\r<BR>\n" );
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document.write( "**4. Solve for P1S**\r<BR>\n" );
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document.write( "* P1S = 200 / cos(62°)<BR>\n" );
document.write( "* cos(62°) ≈ 0.4695\r<BR>\n" );
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document.write( "* P1S = 200 / 0.4695<BR>\n" );
document.write( "* P1S ≈ 425.98 nm\r<BR>\n" );
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document.write( "**5. Round to an Appropriate Number of Decimal Places**\r<BR>\n" );
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document.write( "We can round to two decimal places, as it's a practical distance measurement.\r<BR>\n" );
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document.write( "P1S ≈ 426.00 nm\r<BR>\n" );
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document.write( "**Therefore, the ship traveled approximately 426.00 nautical miles.**<BR>\n" );
document.write( " </SPAN>\n" );
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