An oak tree is 24 feet tall and a bird is standing on the ground 32 feet from the tree. If the bird flies directly to the top of the tree, how far will it fly?

To solve this problem, we can use the Pythagorean theorem, which 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. This can be written as: a² + b² = c².

Here, the height of the tree is one side of the triangle (a), the distance from the bird to the tree is the other side (b), and the distance the bird flies is the hypotenuse (c).

Given: a = 24 feet (height of the tree) b = 32 feet (distance from the bird to the tree)

We need to find c (distance the bird flies).

Using the Pythagorean theorem:

c² = a² + b² c² = (24 feet)² + (32 feet)² c² = 576 feet² + 1024 feet² c² = 1600 feet²

To find c, we take the square root of c²:

c = √1600 feet² c = 40 feet

So, the bird will fly 40 feet to reach the top of the tree.