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, [tex]h^2+ 15^2 = (2h +1)^2[/tex]
Simplifying it down, we get [tex]3h^2+4h-224=0[/tex]
We can use the quadratic formula to solve this, where the solutions are [tex] \frac{-4 \pm \sqrt{4^2 - 4 * 3 * (-224)} }{2*3} = \frac{-4 \pm \sqrt{2704} }{6} = \frac{-4 \pm 52}{6} [/tex]
Therefore the answers are [tex]- \frac{56}{6} [/tex] or [tex] \frac{48}{6} =8[/tex]
The answer is 8 since the height of the tree must be positive.
