To find the angle formed between the pole and the string, we can consider the pole, the string, and the ground as forming a right triangle. In this triangle:
- The height of the pole is one leg of the triangle, which measures 8 feet.
- The length of the string is the hypotenuse of the triangle, which measures 12 feet.
We can denote the angle between the pole and the string as \( \theta \).
We can use the trigonometric function cosine to find this angle:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{12} \]
Calculating this gives:
\[ \cos(\theta) = \frac{2}{3} \approx 0.6667 \]
Now, we can find the angle \( \theta \) by taking the inverse cosine:
\[ \theta = \cos^{-1}\left(\frac{2}{3}\right) \]
Using a calculator:
\[ \theta \approx 48.19^\circ \]
Thus, the approximate angle formed between the pole and the string is:
\[ \boxed{48.2^\circ} \]
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