Question

During a storm, a tree falls toward a house. the top of the tree leans against the top of the house, 16 feet above the ground. the distance on the ground from the house to the base of the tree is 32 feet. what is the height of the tree to the nearest tenth?

Answer 1

The given problem can be exemplified in the following diagram:

Applying the Pythagorean theorem we get:

$h^2=(16ft)^2+(32ft)^2$

Solving the squares:

$h^2=256ft^2+1024ft^2$

Solving the operations:

$h^2=1280ft^2$

Now we take the square root to both sides:

$\sqrt[]{h^2}=\sqrt[]{1280ft^2}$

Solving the operations:

$h=35.8ft$

Therefore, the height of the tree is 35.8 feet.