At a point on the ground $15 \mathrm{ft}$ from the base of a tree, the distance to the top of the tree is $1 \mathrm{ft}$ more than 2 times the height of the tree. Find the height of the tree.

Step 1 ：Let the height of the tree be denoted as \(h\).

Step 2 ：The distance from the point on the ground to the top of the tree is \(2h + 1\).

Step 3 ：The distance from the point on the ground to the base of the tree is 15 feet.

Step 4 ：Using the Pythagorean theorem, we can set up the equation as follows: \((2h + 1)^2 = h^2 + 15^2\).

Step 5 ：Solving this equation gives two possible values for the height of the tree: -28/3 and 8.

Step 6 ：However, the height of a tree cannot be negative, so we discard -28/3.

Step 7 ：Therefore, the height of the tree is \(\boxed{8}\) feet.