Question
A 20 foot tall flag pole casts a shadow that is 15 feet long. which of the following correctly uses the Pythagorean theorem to solve for the distance from the top of the flag pole to the tip of its shadow?
Answers
GPT-4o mini
To find the distance from the top of the flag pole to the tip of its shadow, you can use the Pythagorean theorem. The flag pole and its shadow form a right triangle, where:
- The height of the flag pole is one leg of the triangle (20 feet).
- The length of the shadow is the other leg of the triangle (15 feet).
- The distance from the top of the flag pole to the tip of the shadow is the hypotenuse (let's denote it as \( c \)).
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
In this case, we have:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
- \( c \) is the distance we want to find.
So, we can set up the equation:
\[
20^2 + 15^2 = c^2
\]
Calculating the squares:
\[
400 + 225 = c^2
\]
Adding them together:
\[
625 = c^2
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{625} = 25
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is 25 feet.
- The height of the flag pole is one leg of the triangle (20 feet).
- The length of the shadow is the other leg of the triangle (15 feet).
- The distance from the top of the flag pole to the tip of the shadow is the hypotenuse (let's denote it as \( c \)).
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
In this case, we have:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
- \( c \) is the distance we want to find.
So, we can set up the equation:
\[
20^2 + 15^2 = c^2
\]
Calculating the squares:
\[
400 + 225 = c^2
\]
Adding them together:
\[
625 = c^2
\]
Now, take the square root of both sides to find \( c \):
\[
c = \sqrt{625} = 25
\]
Thus, the distance from the top of the flag pole to the tip of its shadow is 25 feet.