A length of a rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the building is 36 feet tall, how tall is the tree?
A rope stretched between a building and a stake in the ground, with a tree growing halfway between the building and the stake and touching the rope.
(1 point)
Responses
8 feet
8 feet
18 feet
18 feet
11 feet
11 feet
6 feet
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.