SOLUTION: At a point on the ground 15 ft from a base of a tree,the distant to the top of the tree is 1ft more than 2 times the height of the tree find the height of the tree.

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Question 987641: At a point on the ground 15 ft from a base of a tree,the distant to the top of the tree is 1ft more than 2 times the height of the tree find the height of the tree.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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The height and the distance from base (15 feet) are 2 legs of a right triangle.
The hypotenuse is distance from the point 15 ft from base to top of tree,
or 2(height) + 1ft.
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Let a=height; b=distance from base=15 ft; c=hypotenuse=2a+1ft
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a%5E2%2Bb%5E2=c%5E2
a%5E2%2B%2815ft%29%5E2=%282a%2B1ft%29%5E2
a%5E2%2B225ft%5E2=4a%5E2%2B4a%2B1
0=3a%5E2%2B4a-224
0=%28a-8%29%283a%2B28%29
a-8=0 OR 3a%2B28=0
a=8 OR 3a=-28
a=8 OR a=-28%2F3
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So a=8 ft
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ANSWER: The height of the tree is 8 feet.