A length of 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 40 ft tall, how tall is the tree
Since the rope is stretched between the top edge of the building and the stake, the height of the building is the same as the length of the rope.
Let x be the distance from the tree to the stake.
Since the tree is growing halfway between the stake and the building, the distance from the tree to the building is also x.
Using the Pythagorean theorem, the height of the tree (h) can be found using the equation:
h^2 = x^2 + 40^2.
Simplifying the equation, we get:
h^2 = x^2 + 1600.
Taking the square root of both sides, we have:
h = √(x^2 + 1600).
So, the height of the tree is √(x^2 + 1600) feet.