SOLUTION: Lucy is standing next to the General Sherman tree in Sequoia National Park, home of some of the largest trees in the world. The distance from Lucy to the base of the tree is 71 m l

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Question 1153777: Lucy is standing next to the General Sherman tree in Sequoia National Park, home of some of the largest trees in the world. The distance from Lucy to the base of the tree is 71 m less than the height of the tree. If the distance from Lucy to the top of the tree is 1 m more than the height of the tree, how tall is the General Sherman?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


x = height of tree
x+1 = distance from Lucy to top of tree
x-71 = distance from Lucy to base of tree

Assuming the ground is level (NOT a good assumption in the location of the General Sherman tree!), then the three lengths form a right triangle.

%28x%2B1%29%5E2+=+x%5E2%2B%28x-71%29%5E2
x%5E2%2B2x%2B1+=+x%5E2%2Bx%5E2-142x%2B5041
0+=+x%5E2-144x%2B5040
0+=+%28x-60%29%28x-84%29

x+=+60 or x=84

x=60 makes the distance from Lucy to the base of the tree negative, so that solution makes no sense.

ANSWER: The height of the tree is x = 84m.