Question
A bird was sitting 24 feet from the base of an oak tree and flew 30 feet to reach the top of the tree. How tall is the tree?
feet
feet
Answers
GPT-4o mini
To find the height of the oak tree, we can use the Pythagorean theorem. The situation can be described as a right triangle where:
- One leg of the triangle (the distance from the base of the tree to the bird) is 24 feet.
- The hypotenuse (the distance the bird flew to reach the top of the tree) is 30 feet.
- The other leg, which we need to find, represents the height of the tree.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
In our case:
- \(a = 24\) feet (distance from the base of the tree)
- \(c = 30\) feet (the distance the bird flew)
Let \(b\) be the height of the tree. The equation becomes:
\[
24^2 + b^2 = 30^2
\]
Calculating the squares:
\[
576 + b^2 = 900
\]
Now, isolate \(b^2\):
\[
b^2 = 900 - 576
\]
\[
b^2 = 324
\]
Next, take the square root of both sides to find \(b\):
\[
b = \sqrt{324} = 18
\]
Thus, the height of the tree is \( \boxed{18} \) feet.
- One leg of the triangle (the distance from the base of the tree to the bird) is 24 feet.
- The hypotenuse (the distance the bird flew to reach the top of the tree) is 30 feet.
- The other leg, which we need to find, represents the height of the tree.
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle, and \(c\) is the hypotenuse.
In our case:
- \(a = 24\) feet (distance from the base of the tree)
- \(c = 30\) feet (the distance the bird flew)
Let \(b\) be the height of the tree. The equation becomes:
\[
24^2 + b^2 = 30^2
\]
Calculating the squares:
\[
576 + b^2 = 900
\]
Now, isolate \(b^2\):
\[
b^2 = 900 - 576
\]
\[
b^2 = 324
\]
Next, take the square root of both sides to find \(b\):
\[
b = \sqrt{324} = 18
\]
Thus, the height of the tree is \( \boxed{18} \) feet.