Question

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 tree. find the height of the tree.

Answer 1

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
`(-4 \pm √(4^2 - 4 * 3 * (-224)) )/(2*3) = (-4 \pm √(2704) )/(6) = (-4 \pm 52)/(6)`

Therefore the answers are
`- (56)/(6)` or
`(48)/(6) =8`

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