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?(1 point) Responses 13.2 feet 13.2 feet 25 feet 25 feet 35 feet 35 feet 625 feet
Answers
GPT-4o mini
To find the distance from the top of the flagpole to the tip of its shadow, we can use the Pythagorean Theorem.
The flagpole and its shadow form a right triangle, where:
- The height of the flagpole (20 feet) is one leg (a).
- The length of the shadow (15 feet) is the other leg (b).
- The distance from the top of the flagpole to the tip of its shadow is the hypotenuse (c) that we want to find.
According to the Pythagorean Theorem, we have:
\[ a^2 + b^2 = c^2 \]
Substituting the values we have:
\[ (20)^2 + (15)^2 = c^2 \]
Calculating each part:
\[ 400 + 225 = c^2 \]
\[ 625 = c^2 \]
Now, taking the square root of both sides to solve for \( c \):
\[ c = \sqrt{625} \]
\[ c = 25 \text{ feet} \]
So, the distance from the top of the flagpole to the tip of its shadow is **25 feet**.
The flagpole and its shadow form a right triangle, where:
- The height of the flagpole (20 feet) is one leg (a).
- The length of the shadow (15 feet) is the other leg (b).
- The distance from the top of the flagpole to the tip of its shadow is the hypotenuse (c) that we want to find.
According to the Pythagorean Theorem, we have:
\[ a^2 + b^2 = c^2 \]
Substituting the values we have:
\[ (20)^2 + (15)^2 = c^2 \]
Calculating each part:
\[ 400 + 225 = c^2 \]
\[ 625 = c^2 \]
Now, taking the square root of both sides to solve for \( c \):
\[ c = \sqrt{625} \]
\[ c = 25 \text{ feet} \]
So, the distance from the top of the flagpole to the tip of its shadow is **25 feet**.