Question
A 30 foot tall tree casts a shadow that is 16 feet long. What is the distance from the top of the tree to the top of it's shadow?
Apply a Pythagorean triple to solve this problem.
14ft
15ft
17ft
34ft
Apply a Pythagorean triple to solve this problem.
14ft
15ft
17ft
34ft
Answers
GPT-4o mini
To find the distance from the top of the tree to the top of its shadow, we can visualize this 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 distance from the top of the tree to the top of the shadow represents the hypotenuse.
Given:
- Height of the tree (one leg of the triangle) = 30 feet
- Length of the shadow (the other leg of the triangle) = 16 feet
Using the Pythagorean theorem, we know:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(c\) is the hypotenuse, \(a\) is one leg (the height), and \(b\) is the other leg (the shadow length).
So in our case:
- \(a = 30\)
- \(b = 16\)
Calculating \(c\):
\[
c = \sqrt{30^2 + 16^2}
\]
\[
c = \sqrt{900 + 256}
\]
\[
c = \sqrt{1156}
\]
\[
c = 34
\]
The distance from the top of the tree to the top of its shadow is therefore 34 feet.
Among the options given (14ft, 15ft, 17ft, 34ft), the answer is **34ft**.
Given:
- Height of the tree (one leg of the triangle) = 30 feet
- Length of the shadow (the other leg of the triangle) = 16 feet
Using the Pythagorean theorem, we know:
\[
c = \sqrt{a^2 + b^2}
\]
Where \(c\) is the hypotenuse, \(a\) is one leg (the height), and \(b\) is the other leg (the shadow length).
So in our case:
- \(a = 30\)
- \(b = 16\)
Calculating \(c\):
\[
c = \sqrt{30^2 + 16^2}
\]
\[
c = \sqrt{900 + 256}
\]
\[
c = \sqrt{1156}
\]
\[
c = 34
\]
The distance from the top of the tree to the top of its shadow is therefore 34 feet.
Among the options given (14ft, 15ft, 17ft, 34ft), the answer is **34ft**.