To determine the distance from the base of the tent pole to where the rope is anchored on the ground, we can visualize this situation using a right triangle. The height of the tent pole represents one leg of the triangle, the length of the rope represents the hypotenuse, and the distance from the base of the pole to the point on the ground where the rope is anchored represents the other leg.
Let's denote:
- The height of the tent pole as \( a = 8 \) feet.
- The length of the rope as \( c = 17 \) feet.
- The distance along the ground from the tent pole to the rope as \( b \).
According to the Pythagorean theorem, we can state:
\[ a^2 + b^2 = c^2 \]
Plugging in the values we have:
\[ 8^2 + b^2 = 17^2 \]
Calculating the squares:
\[ 64 + b^2 = 289 \]
Next, we solve for \( b^2 \):
\[ b^2 = 289 - 64 \] \[ b^2 = 225 \]
Now take the square root of both sides to find \( b \):
\[ b = \sqrt{225} = 15 \]
Therefore, the distance from the tent pole to the end of the rope along the ground is \( \boxed{15} \) feet.
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