Question
A 24-foot-tall tree casts a shadow that is 10 feet long. What is the distance from the top of the tree to the top of its shadow? Apply a Pythagorean triple to solve this problem.(1 point)
feet
feet
Answers
GPT-4o mini
To find the distance from the top of the tree to the top of its shadow, we can visualize this scenario as a right triangle.
Here, the height of the tree is one leg of the triangle (24 feet), and the length of the shadow is the other leg of the triangle (10 feet). The distance from the top of the tree to the top of the shadow will be the hypotenuse of this right triangle.
We can apply the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse.
In our case:
- \(a = 24\) feet (height of the tree)
- \(b = 10\) feet (length of the shadow)
Plugging in these values:
\[
24^2 + 10^2 = c^2
\]
Calculating the squares:
\[
576 + 100 = c^2
\]
\[
676 = c^2
\]
Now, taking the square root of both sides to find \(c\):
\[
c = \sqrt{676} = 26
\]
Thus, the distance from the top of the tree to the top of its shadow is **26 feet**.
Here, the height of the tree is one leg of the triangle (24 feet), and the length of the shadow is the other leg of the triangle (10 feet). The distance from the top of the tree to the top of the shadow will be the hypotenuse of this right triangle.
We can apply the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(a\) and \(b\) are the legs of the triangle and \(c\) is the hypotenuse.
In our case:
- \(a = 24\) feet (height of the tree)
- \(b = 10\) feet (length of the shadow)
Plugging in these values:
\[
24^2 + 10^2 = c^2
\]
Calculating the squares:
\[
576 + 100 = c^2
\]
\[
676 = c^2
\]
Now, taking the square root of both sides to find \(c\):
\[
c = \sqrt{676} = 26
\]
Thus, the distance from the top of the tree to the top of its shadow is **26 feet**.