To find the distance from the top of the flagpole to the tip of its shadow, we can use the Pythagorean Theorem. The flagpole, the shadow, and the line from the top of the flagpole to the tip of the shadow form a right triangle.
Let's denote the height of the flagpole as \( a = 20 \) feet, the length of the shadow as \( b = 15 \) feet, and the distance we want to find (the hypotenuse) as \( c \).
According to the Pythagorean Theorem:
\[ c^2 = a^2 + b^2 \]
Substituting the values:
\[ c^2 = 20^2 + 15^2 \] \[ c^2 = 400 + 225 \] \[ c^2 = 625 \]
Now, we take the square root of both sides 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.