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?
a. 625 feet
b. 13.2 feet
c. 35 feet
d. 25 feet
a. 625 feet
b. 13.2 feet
c. 35 feet
d. 25 feet
Answers
GPT-4o mini
To solve for the distance from the top of the flag pole to the tip of its shadow using the Pythagorean Theorem, we can model the situation as a right triangle.
In this case:
- The height of the flag pole (20 feet) represents one leg of the triangle.
- The length of the shadow (15 feet) represents the other leg of the triangle.
- The distance from the top of the flag pole to the tip of its shadow represents the hypotenuse.
We can denote:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
- \( c \) is the distance we want to find (the hypotenuse).
According to the Pythagorean Theorem:
\[ c^2 = a^2 + b^2 \]
Plugging in our values:
\[ c^2 = 20^2 + 15^2 \]
\[ c^2 = 400 + 225 \]
\[ c^2 = 625 \]
\[ c = \sqrt{625} \]
\[ c = 25 \]
So, the distance from the top of the flag pole to the tip of its shadow is 25 feet.
Therefore, the correct answer is **d. 25 feet**.
In this case:
- The height of the flag pole (20 feet) represents one leg of the triangle.
- The length of the shadow (15 feet) represents the other leg of the triangle.
- The distance from the top of the flag pole to the tip of its shadow represents the hypotenuse.
We can denote:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
- \( c \) is the distance we want to find (the hypotenuse).
According to the Pythagorean Theorem:
\[ c^2 = a^2 + b^2 \]
Plugging in our values:
\[ c^2 = 20^2 + 15^2 \]
\[ c^2 = 400 + 225 \]
\[ c^2 = 625 \]
\[ c = \sqrt{625} \]
\[ c = 25 \]
So, the distance from the top of the flag pole to the tip of its shadow is 25 feet.
Therefore, the correct answer is **d. 25 feet**.