document.write( "Question 1208415: A person who is 6 feet tall is standing on the beach in Florida and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?\r
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\n" ); document.write( "\n" ); document.write( "d = distance the ship is from shore\r
\n" ); document.write( "\n" ); document.write( "r = radius of Earth = 3960 miles\r
\n" ); document.write( "\n" ); document.write( "m = number of feet in a mile = 5280\r
\n" ); document.write( "\n" ); document.write( "h = height of the person standing on the beach in Florida \r
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\n" ); document.write( "\n" ); document.write( "d^2 + r^2 = [(r + (h/m)]^2\r
\n" ); document.write( "\n" ); document.write( "We want d.\r
\n" ); document.write( "\n" ); document.write( "d^2 + (3960)^2 = [(3960) + (6/5280)]^2\r
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Algebra.Com's Answer #846819 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Make a sketch. The Earth is a sphere (not flat) - so, draw a circle representing the spherical Earth\r\n" );
document.write( "of the radius  r = 3960 miles.\r\n" );
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document.write( "On the top of the circle, draw a person h = 6 ft =  miles tall, standing on the Earth.\r\n" );
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document.write( "From the level of the person's head, draw a tangent line to the Earth.\r\n" );
document.write( "This tangent line will represent how far this person sees the surface of the ocean.\r\n" );
document.write( "Also, draw the radius of the Earth to the tangent point. \r\n" );
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document.write( "On the sketch, you will see the right-angled triangle with the hypotenuse length of\r\n" );
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document.write( "      r + h = 3960 +  miles\r\n" );
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document.write( "and one leg of the length  r = 3960 miles.\r\n" );
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document.write( "So, you can find the other leg of this triangle, which is a tangent to the Earth surface, \r\n" );
document.write( "from the Pythagorean equation\r\n" );
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document.write( "   d^2 + r^2 = (r + h)^2.\r\n" );
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document.write( "Here \"d\" is the distance to the horizon, in miles.\r\n" );
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document.write( "So, your friend is right.\r\n" );
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document.write( "Calculations give  d =  = 3 miles.\r\n" );
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