Question
A 20 foot tall flag pole casts a shadow that is 15 feet long. Which of the following correctly uses Pythagorean theorem to solve for the distance from the top of the flag pole to the tip of its shadow?
625 feet
25 feet
35 feet
13.2 feet
625 feet
25 feet
35 feet
13.2 feet
Answers
GPT-4o mini
To solve for the distance from the top of the flagpole to the tip of its shadow using the Pythagorean theorem, we can set up the problem as follows:
1. The height of the flagpole (one leg of the right triangle) is 20 feet.
2. The length of the shadow (the other leg of the right triangle) is 15 feet.
3. The distance from the top of the flagpole to the tip of its shadow is the hypotenuse.
Let \( c \) be the length of the hypotenuse. According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \( a \) is the height of the flagpole and \( b \) is the length of the shadow. Thus, we plug in the values:
\[
c^2 = 20^2 + 15^2
\]
Calculating the squares:
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{625} = 25
\]
So the distance from the top of the flagpole to the tip of its shadow is **25 feet**.
Therefore, the correct answer is **25 feet**.
1. The height of the flagpole (one leg of the right triangle) is 20 feet.
2. The length of the shadow (the other leg of the right triangle) is 15 feet.
3. The distance from the top of the flagpole to the tip of its shadow is the hypotenuse.
Let \( c \) be the length of the hypotenuse. According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \( a \) is the height of the flagpole and \( b \) is the length of the shadow. Thus, we plug in the values:
\[
c^2 = 20^2 + 15^2
\]
Calculating the squares:
\[
c^2 = 400 + 225
\]
\[
c^2 = 625
\]
Now, take the square root to find \( c \):
\[
c = \sqrt{625} = 25
\]
So the distance from the top of the flagpole to the tip of its shadow is **25 feet**.
Therefore, the correct answer is **25 feet**.