document.write( "Question 1207217: A person standing 400 ft from the base of a mountain measures the angle of elevation from the ground to the top of the mountain to be 25° The person then walks 500 ft straight back and measures the angle of elevation to now be 20°. How tall is the mountain?
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Algebra.Com's Answer #844962 by ikleyn(52818) $\"\"$ $\"About$

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\n" ); document.write( "A person standing 400 ft from the base of a mountain measures the angle of elevation
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @Theo is INCORRECT.\r
\n" ); document.write( "\n" ); document.write( "        400 feet that Theo marked in his plot, represents, actually, the base of the mountain, which is NOT GIVEN in the problem.\r
\n" ); document.write( "\n" ); document.write( "        Actually, this data of 400 feet plays small role in this problem (if any) and only confuses a reader.\r
\n" ); document.write( "\n" ); document.write( "        The data which really PLAYS a role is 500 feet, the distance between the two positions.\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "Let L be the distance (on the ground level, i.e. horizontally) from the first position to the \r\n" );
document.write( "top of the mountain. So, we can write\r\n" );
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document.write( "     = tan(25°),  or  x = tan(25°)*L.   (1)\r\n" );
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document.write( "where x is the height of the mountain.\r\n" );
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document.write( "Then the distance (on the ground level, i.e. horizontally) from the second position to the \r\n" );
document.write( "top of the mountain is  (L+500) feet. So, we can write\r\n" );
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document.write( "     = tan(20°),  or x = tan(20°)*(L+500).  (2)\r\n" );
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document.write( "In equations (1) and (2) left sides are identical, so their right side are equal\r\n" );
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document.write( "    tan(25°)*L = tan(20°)*(L+500).\r\n" );
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document.write( "Simplify and find L\r\n" );
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document.write( "    tan(25°)*L = tan(20°)*L + 500*tan(20°),\r\n" );
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document.write( "    tan(25°) - tan(20°)*L = 500*tan(20°),\r\n" );
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document.write( "    L = .\r\n" );
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document.write( "Now substitute it into equation (1) and find x\r\n" );
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document.write( "    x =  =  = 829.228 ft.\r\n" );
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document.write( "Round to the closest nearest whole foot and get the\r\n" );
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document.write( "ANSWER.  The height of the mountain is about 829 feet.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (correctly).\r
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\n" ); document.write( "\n" ); document.write( "To see many other solved similar and different problems of the type \" find the height \",
\n" ); document.write( "look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Find the height \r
\n" ); document.write( "\n" ); document.write( "in this site (free of charge).\r
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there.\r
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