document.write( "Question 658844: from 2 point south of a hill on a level ground and are 1000ft apart, the angels of elevation of the hill are 12º20' and 82º40'. how high is the hill? \n" ); document.write( "
Algebra.Com's Answer #410500 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "The following depicts the situation.  (The figure is not drawn to scale.)\r\n" );
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document.write( "The two small circles indicate the two points on level ground\r\n" );
document.write( "which are 1000 feet apart.  We want to find y, the height of \r\n" );
document.write( "the hill.\r\n" );
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document.write( "There are two right triangles involved here. They are these:\r\n" );
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document.write( "and\r\n" );
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document.write( "In the first right triangle the side opposite the 12°20' angle is y,\r\n" );
document.write( "and the side adjacent the 12°20' is 1000+x, so using the fact that\r\n" );
document.write( "tangent =  we have the equation\r\n" );
document.write( "from the first right triangle:\r\n" );
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document.write( "tan(12°80') = \r\n" );
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document.write( "In the second right triangle the side opposite the 82°40' angle is y,\r\n" );
document.write( "and the side adjacent the 82°40' is x, so again using the fact that\r\n" );
document.write( "tangent =  we have the equation\r\n" );
document.write( "from the second triangle:\r\n" );
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document.write( "tan(82°40') = \r\n" );
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document.write( "To keep from getting bogged down in notation,\r\n" );
document.write( "since those tangents are bulky to write let's let\r\n" );
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document.write( "A = tan(12°20') and B = tan(82°40')\r\n" );
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document.write( "Then the equations look simpler as:\r\n" );
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document.write( "A =  \r\n" );
document.write( "B = \r\n" );
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document.write( "Multiplying both through by their denominators:\r\n" );
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document.write( "A(1000+x) = y\r\n" );
document.write( "       Bx = y\r\n" );
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document.write( "We want y, not x, so we solve for x.\r\n" );
document.write( "Solving the second equation for x:\r\n" );
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document.write( "        x = \r\n" );
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document.write( "Substituting in the first equation:\r\n" );
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document.write( "A(1000+) = y\r\n" );
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document.write( "Distribute:\r\n" );
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document.write( "1000A +  = y\r\n" );
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document.write( "Multiply through by B\r\n" );
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document.write( "1000AB + Ay = By\r\n" );
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document.write( "Get both terms in y on the right side:\r\n" );
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document.write( "1000AB = By - Ay\r\n" );
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document.write( "Factor out y on the right\r\n" );
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document.write( "1000AB = y(B - A)\r\n" );
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document.write( "Divide both sides by (B - A)\r\n" );
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document.write( " = y\r\n" );
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document.write( "Now substitute A = tan(12°20') and B = tan(82°40') \r\n" );
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document.write( " = y\r\n" );
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document.write( "That works out to be 224.9752003 or \r\n" );
document.write( "the hill is about 225 feet high.\r\n" );
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document.write( "Edwin
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