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)
Apply a Pythagorean triple to solve this problem. (1 point)
Answers
GPT-4o mini
To find the distance from the top of the tree to the top of its shadow, we can use the Pythagorean theorem. The tree's height and the length of the shadow form a right triangle, where:
- The height of the tree (24 feet) is one leg of the triangle.
- The length of the shadow (10 feet) is the other leg of the triangle.
- The distance from the top of the tree to the top of its shadow is the hypotenuse.
We can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the two legs of the triangle, and \( c \) is the hypotenuse.
In this case:
- \( a = 24 \) feet
- \( b = 10 \) feet
Now we calculate \( c \):
\[
c^2 = 24^2 + 10^2
\]
Calculating the squares:
\[
24^2 = 576
\]
\[
10^2 = 100
\]
Now we add them together:
\[
c^2 = 576 + 100 = 676
\]
Now we take the square root to find \( c \):
\[
c = \sqrt{676} = 26
\]
Thus, the distance from the top of the tree to the top of its shadow is \( \boxed{26} \) feet.
- The height of the tree (24 feet) is one leg of the triangle.
- The length of the shadow (10 feet) is the other leg of the triangle.
- The distance from the top of the tree to the top of its shadow is the hypotenuse.
We can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the two legs of the triangle, and \( c \) is the hypotenuse.
In this case:
- \( a = 24 \) feet
- \( b = 10 \) feet
Now we calculate \( c \):
\[
c^2 = 24^2 + 10^2
\]
Calculating the squares:
\[
24^2 = 576
\]
\[
10^2 = 100
\]
Now we add them together:
\[
c^2 = 576 + 100 = 676
\]
Now we take the square root to find \( c \):
\[
c = \sqrt{676} = 26
\]
Thus, the distance from the top of the tree to the top of its shadow is \( \boxed{26} \) feet.