Bot GPT 4-o mini To find the distance from the top of the flag pole to the tip of its shadow, we can represent this situation as a right triangle. The height of the flag pole is one side (the vertical side), the length of the shadow is the other side (the horizontal side), and the distance from the top of the flag pole to the tip of the shadow is the hypotenuse.
Let's denote:
- The height of the flag pole (vertical side) = 20 feet
- The length of the shadow (horizontal side) = 15 feet
- The distance from the top of the flag pole to the tip of the shadow (hypotenuse) = \( c \)
According to the Pythagorean theorem, we have:
\[ a^2 + b^2 = c^2 \]
Where:
- \( a = 20 \) feet (height of the flag pole)
- \( b = 15 \) feet (length of the shadow)
Plugging in the values:
\[ 20^2 + 15^2 = c^2 \]
Calculating \( 20^2 \) and \( 15^2 \):
\[ 400 + 225 = c^2 \]
Now, add them together:
\[ 625 = c^2 \]
To find \( c \), take the square root of both sides:
\[ c = \sqrt{625} = 25 \text{ feet} \]
Therefore, the distance from the top of the flag pole to the tip of its shadow is 25 feet.
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