Question
A 25-foot-tall flag pole casts a shadow that is 18 feet long. Which of the following correctly uses the Pythagorean Theorem to sole for the distance from the top of the flag pole to the tip of its shadow?
a. 308 feet
b. 30.8 feet
c. 43 feet
d. 17.3 feet
a. 308 feet
b. 30.8 feet
c. 43 feet
d. 17.3 feet
Answers
GPT-4o mini
To determine the distance from the top of the flag pole to the tip of its shadow using the Pythagorean theorem, we can think of this situation as a right triangle. The height of the flag pole is one leg of the triangle, the length of the shadow is the other leg, and the distance we want to find is the hypotenuse.
Let's denote:
- The height of the flag pole as \( a = 25 \) feet
- The length of the shadow as \( b = 18 \) feet
- The distance from the top of the flag pole to the tip of its shadow as \( c \)
According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the known values:
\[
c^2 = (25)^2 + (18)^2
\]
\[
c^2 = 625 + 324
\]
\[
c^2 = 949
\]
To find \( c \), we take the square root of both sides:
\[
c = \sqrt{949}
\]
Calculating \( \sqrt{949} \):
\[
c \approx 30.8 \text{ feet}
\]
Therefore, the correct answer is:
**b. 30.8 feet**
Let's denote:
- The height of the flag pole as \( a = 25 \) feet
- The length of the shadow as \( b = 18 \) feet
- The distance from the top of the flag pole to the tip of its shadow as \( c \)
According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the known values:
\[
c^2 = (25)^2 + (18)^2
\]
\[
c^2 = 625 + 324
\]
\[
c^2 = 949
\]
To find \( c \), we take the square root of both sides:
\[
c = \sqrt{949}
\]
Calculating \( \sqrt{949} \):
\[
c \approx 30.8 \text{ feet}
\]
Therefore, the correct answer is:
**b. 30.8 feet**