document.write( "Question 1195838: 1.) F is the position of the sounding boat at the time a given sounding is made and E, C and D are the three shore points. EC = 1200m, CD = 965m, ∠ECD = 146°30’, ∠EFC = 28°15’ and ∠CFD = 22°30’. Find the distance DF.\r
\n" ); document.write( "\n" ); document.write( "2.) How far apart are two points on the equator one in longitude 40 degrees East and the other in longitude 150 degrees West?\r
\n" ); document.write( "\n" ); document.write( "3.) An airplane leaves Guam (13°24’ N, 114°38’ E) with an initial course of 36°40’ for a great-circle track. Locate the point of the great circle track which is nearest to the north pole. \n" ); document.write( "

Algebra.Com's Answer #828412 by ikleyn(52903) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "(2) How far apart are two points on the equator one in longitude 40 degrees East and the other in longitude 150 degrees West?
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\n" ); document.write( "\n" ); document.write( "Usually, such problems go with the given value for the Earth radius.\r
\n" ); document.write( "\n" ); document.write( "But, since the current problem is so special that does not give the value,\r
\n" ); document.write( "\n" ); document.write( "I will refer to this Wikipedia info https://en.wikipedia.org/wiki/Earth_radius\r
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document.write( "    Earth radius (denoted as ) is the distance from the center of Earth \r\n" );
document.write( "    to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, \r\n" );
document.write( "    the radius ranges from a maximum of nearly 6,378 km (equatorial radius) \r\n" );
document.write( "    to a minimum of nearly 6,357 km (polar radius).\r\n" );
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document.write( "    A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, \r\n" );
document.write( "    which is recommended by the International Astronomical Union to be the equatorial value.\r\n" );
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document.write( "    A globally-average value is usually considered to be 6,371 kilometres with a 0.3% variability (±10 km).\r\n" );
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\n" ); document.write( "\n" ); document.write( "After this introduction, my solution is below.\r
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document.write( "One point is 40 degrees East along the equator from the zero meridian.\r\n" );
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document.write( "The other point is 150 degrees West along the equator from the zero meridian.\r\n" );
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document.write( "So, the central angle between these points is 40 + 150 = 190 degrees.\r\n" );
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document.write( "Since this angle is greater than 180 degrees, it is, obviously, the major central angle.\r\n" );
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document.write( "Since the question is about the distance between the points along the equator, we should take \r\n" );
document.write( "a MINOR central angle, which complements 190 degrees to 360 degrees, i.e. 360-190 = 170 degrees.\r\n" );
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document.write( "Then the distance between the points is  d =  = 18,894 kilometers\r\n" );
document.write( "(rounded to the closest kilometer).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "In the future, please do not pack more than one problem per post.\r
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\n" ); document.write( "\n" ); document.write( "It is prohibited by the rules of this forum, and it ALWAYS works AGAINST your own interests.\r
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\n" ); document.write( "\n" ); document.write( "About the rules of this forum, please read web-page\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/\r
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\n" ); document.write( "\n" ); document.write( "from which you post your problems.\r
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\n" ); document.write( "\n" ); document.write( "In your post, coordinates of Guam island in problem (3) are FATALLY INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "In reality, they are TOTALLY different.\r
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\n" ); document.write( "\n" ); document.write( "See Wikipedia, https://en.wikipedia.org/wiki/Guam\r
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