document.write( "Question 1161443: At a certain time of day, a tree that is x meters tall casts a shadow that is x−21 meters long. If the distance from the top of the tree to the end of the shadow is x+3 meters long, what is the height, x, of the tree? \n" ); document.write( "

Algebra.Com's Answer #784995 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Assuming the tree is on level ground, the tree, its shadow, and the line from the top of the tree to the tip of the shadow form a right triangle. So use the Pythagorean Theorem with the given expressions.

\n" ); document.write( " $\"%28x%2B3%29%5E2+=+x%5E2%2B%28x-21%29%5E2\"$

\n" ); document.write( " $\"x%5E2%2B6x%2B9+=+x%5E2%2Bx%5E2-42x%2B441\"$

\n" ); document.write( " $\"0+=+x%5E2-48x%2B432\"$

\n" ); document.write( " $\"0+=+%28x-36%29%28x-12%29\"$

\n" ); document.write( " $\"x+=+36\"$ or $\"x+=+12\"$

\n" ); document.write( "With x-21 as the length of the shadow, x=12 makes no sense. So

\n" ); document.write( "ANSWER:
\n" ); document.write( "height of tree = x = 36m
\n" ); document.write( "length of shadow = x-21 = 15m
\n" ); document.write( "distance from top of tree to tip of shadow = x+3 = 39m

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