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
Answers
GPT-4o mini
To solve the problem, we can visualize the situation as a right triangle where:
- The vertical leg is the height of the tree (24 feet).
- The horizontal leg is the length of the shadow (10 feet).
- The hypotenuse is the distance from the top of the tree to the top of its shadow.
We can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
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)
Now, we can plug in the values:
\[
24^2 + 10^2 = c^2
\]
Calculating the squares:
\[
576 + 100 = c^2
\]
\[
676 = c^2
\]
Now, take the square root of both sides to 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**.
- The vertical leg is the height of the tree (24 feet).
- The horizontal leg is the length of the shadow (10 feet).
- The hypotenuse is the distance from the top of the tree to the top of its shadow.
We can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
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)
Now, we can plug in the values:
\[
24^2 + 10^2 = c^2
\]
Calculating the squares:
\[
576 + 100 = c^2
\]
\[
676 = c^2
\]
Now, take the square root of both sides to 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**.