SOLUTION: At a point on the ground 24 ft from the base of a​ tree, the distance to the top of the tree is 6 ft more than 2 times the height of the tree. Find the height of the tree.
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Question 1066605: At a point on the ground 24 ft from the base of a tree, the distance to the top of the tree is 6 ft more than 2 times the height of the tree. Find the height of the tree.
The height of the tree is
blank ft.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Drawing this helps.
there is a triangle with leg 24, the tree height x, and the hypotenuse 2x+6.
x^2+576=(2x+6)^2=4x^2+24x+36
0=3x^2+24x-540
0=x^2+8x-180
0=(x+18)(x-10)
positive root ix x=10 feet, height of tree. ANSWER
from 24 feet away, the distance to the top is 10^2+24^2=676=26^2, which is 6 feet more than twice the height of the tree.
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