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?(5 points)
Answers
GPT-4o mini
To find the distance from the top of a 24-foot tall tree to the top of its 10-foot long shadow, we can visualize this situation as a right triangle. The height of the tree represents one vertical leg of the triangle, and the length of the shadow represents the horizontal leg of the triangle. We will use the Pythagorean theorem to find the distance.
Let:
- \( h = 24 \) feet (height of the tree)
- \( s = 10 \) feet (length of the shadow)
- \( d \) be the distance from the top of the tree to the top of its shadow
According to the Pythagorean theorem:
\[
d^2 = h^2 + s^2
\]
Substituting in the values we have:
\[
d^2 = 24^2 + 10^2
\]
\[
d^2 = 576 + 100
\]
\[
d^2 = 676
\]
Now, we take the square root of both sides to find \( d \):
\[
d = \sqrt{676}
\]
\[
d = 26 \text{ feet}
\]
Therefore, the distance from the top of the tree to the top of its shadow is **26 feet**.
Let:
- \( h = 24 \) feet (height of the tree)
- \( s = 10 \) feet (length of the shadow)
- \( d \) be the distance from the top of the tree to the top of its shadow
According to the Pythagorean theorem:
\[
d^2 = h^2 + s^2
\]
Substituting in the values we have:
\[
d^2 = 24^2 + 10^2
\]
\[
d^2 = 576 + 100
\]
\[
d^2 = 676
\]
Now, we take the square root of both sides to find \( d \):
\[
d = \sqrt{676}
\]
\[
d = 26 \text{ feet}
\]
Therefore, the distance from the top of the tree to the top of its shadow is **26 feet**.