document.write( "Question 1048375: To determine the height AB of a tree, Nancy places a mirror on the ground at E. From E, she walks backwards to a point D, where she is just about to see the top of the tree in the mirror. Given BE=18m,ED=2.4m, angle CED = angle AEB, and that her eyes are 1.6 m off the ground, find the height of the tree.\r
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Algebra.Com's Answer #663944 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "To determine the height AB of a tree, Nancy places a mirror on the ground at E. From E, she walks backwards to a point D,
\n" ); document.write( "where she is just about to see the top of the tree in the mirror. Given BE=18m, ED=2.4m, angle CED = angle AEB,
\n" ); document.write( "and that her eyes are 1.6 m off the ground, find the height of the tree.\r
\n" ); document.write( "\n" ); document.write( "The answer is 12m, I don't get how!
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document.write( "Make a sketch, please.\r\n" );
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document.write( "The point B is on the ground, where the tree is standing.\r\n" );
document.write( "The point A is the top of the tree.\r\n" );
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document.write( "The point D is on the ground, where Nancy is standing.\r\n" );
document.write( "The point C is where Nancy's eyes are.\r\n" );
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document.write( "The triangles BAE and DCE are similar.\r\n" );
document.write( "Why? They are right-angled triangles, and, in addition, you are given that\r\n" );
document.write( "angle CED = angle AEB.  (The last is the Reflection Law for a mirror).\r\n" );
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document.write( "Since the triangles are similar, their corresponding sides are proportional:\r\n" );
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document.write( " = .\r\n" );
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document.write( "Substitute the given data. You will get\r\n" );
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document.write( " = .\r\n" );
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document.write( "Find the unknown value of |AB| from this proportion.\r\n" );
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document.write( "|AB| =  = 12 m (coincides with your answer !)\r\n" );
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document.write( "Now you know why.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On triangles similarity, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Similar triangles \r
\n" ); document.write( "\n" ); document.write( "    - Similarity tests for triangles \r
\n" ); document.write( "\n" ); document.write( "    - Proofs of Similarity tests for triangles \r
\n" ); document.write( "\n" ); document.write( "    - In a triangle a straight line parallel to its side cuts off a similar triangle \r
\n" ); document.write( "\n" ); document.write( "    - Problems on similar triangles \r
\n" ); document.write( "\n" ); document.write( "    - Similarity tests for right-angled triangles \r
\n" ); document.write( "\n" ); document.write( "    - Problems on similarity for right-angled triangles\r
\n" ); document.write( "\n" ); document.write( "    - Problems on similarity for right-angled and acute triangles \r
\n" ); document.write( "\n" ); document.write( "    - One property of a median in a triangle \r
\n" ); document.write( "\n" ); document.write( "    - One property of a trapezoid \r
\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on similar triangles \r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on similar triangles \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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