At a point on the ground $70 \mathrm{ft}$ from the base of a tree, the distance to the top of the tree is $2 \mathrm{ft}$ more than 3 times the height of the tree. Find the height of the tree.
The height of the tree is $\mathrm{ft}$.
(Simplify your answer. Round to the nearest foot as needed.)
Answer
Final Answer: The height of the tree is \(\boxed{24}\) feet.
Step 1 ：This problem can be solved using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 2 ：We can write the equation as follows: \((3h+2)^2 = h^2 + 70^2\), where h is the height of the tree.
Step 3 ：We can solve this equation for h to find the height of the tree.
Step 4 ：The solutions to the equation are -51/2 and 24. However, the height of a tree cannot be negative, so the height of the tree is 24 feet.
Step 5 ：Final Answer: The height of the tree is \(\boxed{24}\) feet.
