To find the distance from the top of the flag pole to the tip of its shadow using the Pythagorean theorem, we can set up a right triangle where:
- The height of the flag pole (adjacent side) is 20 feet.
- The length of the shadow (base) is 15 feet.
- The distance from the top of the flag pole to the tip of its shadow (hypotenuse) is what we want to find.
According to the Pythagorean theorem, we have:
\[ a^2 + b^2 = c^2 \]
where:
- \(a = 20\) feet (height of the pole)
- \(b = 15\) feet (length of the shadow)
- \(c\) is the distance we want to find.
Plugging in the values:
\[ 20^2 + 15^2 = c^2 \] \[ 400 + 225 = c^2 \] \[ 625 = c^2 \]
Now, take the square root to find \(c\):
\[ c = \sqrt{625} = 25 \text{ feet} \]
Thus, the distance from the top of the flag pole to the tip of its shadow is 25 feet.
The correct response is:
25 feet