SOLUTION: 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 l

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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?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

%28x%2B3%29%5E2+=+x%5E2%2B%28x-21%29%5E2

x%5E2%2B6x%2B9+=+x%5E2%2Bx%5E2-42x%2B441

0+=+x%5E2-48x%2B432

0+=+%28x-36%29%28x-12%29

x+=+36 or x+=+12

With x-21 as the length of the shadow, x=12 makes no sense. So

ANSWER:
height of tree = x = 36m
length of shadow = x-21 = 15m
distance from top of tree to tip of shadow = x+3 = 39m