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 the situation as a right triangle. The height of the tree represents one leg of the triangle, the length of the shadow represents the other leg, and the line from the top of the tree to the top of the shadow represents the hypotenuse.
Here, the height of the tree is 24 feet, and the length of the shadow is 10 feet. Thus, we label these:
- Height of the tree (one leg of the triangle) = 24 feet
- Length of the shadow (the other leg of the triangle) = 10 feet
Using the Pythagorean theorem, we can find the length of the hypotenuse \(c\):
\[
c^2 = a^2 + b^2
\]
where \(a = 24\) feet and \(b = 10\) feet.
Calculating \(c^2\):
\[
c^2 = 24^2 + 10^2
\]
\[
c^2 = 576 + 100
\]
\[
c^2 = 676
\]
Now, we'll find \(c\):
\[
c = \sqrt{676} = 26 \text{ feet}
\]
Therefore, the distance from the top of the tree to the top of its shadow is **26 feet**.
Here, the height of the tree is 24 feet, and the length of the shadow is 10 feet. Thus, we label these:
- Height of the tree (one leg of the triangle) = 24 feet
- Length of the shadow (the other leg of the triangle) = 10 feet
Using the Pythagorean theorem, we can find the length of the hypotenuse \(c\):
\[
c^2 = a^2 + b^2
\]
where \(a = 24\) feet and \(b = 10\) feet.
Calculating \(c^2\):
\[
c^2 = 24^2 + 10^2
\]
\[
c^2 = 576 + 100
\]
\[
c^2 = 676
\]
Now, we'll find \(c\):
\[
c = \sqrt{676} = 26 \text{ feet}
\]
Therefore, the distance from the top of the tree to the top of its shadow is **26 feet**.