To solve this problem, we can use the concept of similar triangles. Let's call the height of the tree "h" feet.
Since the tree is growing halfway between the stake and the building, we can say that the distance from the tree to the stake is the same as the distance from the tree to the building. Let's call this distance "x" feet.
Now, we can set up a proportion using the similar triangles formed by the building, the tree, and the stake.
We have:
height of building / distance from building to tree = height of tree / distance from tree to stake
Therefore,
36 / x = h / x
Simplifying this proportion, we get:
36 = h
So the height of the tree is 36 feet.