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katrin [286]
2 years ago
14

at a point on the ground 15 ft from the tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tr

ee. find the height of the tree.

Mathematics
1 answer:
muminat2 years ago
7 0
Let's say the tree is of height h. The point 15 ft away, the base of the tree, and the height of the tree form a right triangle, where the length of the sides are h, 2h + 1, and 15 (see attached image).

Using the Pythagorean theorem, h^2+ 15^2 = (2h +1)^2

Simplifying it down, we get 3h^2+4h-224=0

We can use the quadratic formula to solve this, where the solutions are \frac{-4 \pm \sqrt{4^2 - 4 * 3 * (-224)} }{2*3} = \frac{-4 \pm \sqrt{2704} }{6} =  \frac{-4 \pm 52}{6}

Therefore the answers are - \frac{56}{6} or \frac{48}{6} =8

The answer is 8 since the height of the tree must be positive.

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