To find the angle formed where the rope is fastened to the ground, we can use the sine function, which relates the opposite side (the height of the pole) to the hypotenuse (the length of the rope).
In this case:
- The height of the pole (opposite side) = 5 feet
- The length of the rope (hypotenuse) = 8 feet
We can use the sine function:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{8} \]
Next, we will find the angle \(\theta\) using the inverse sine function (\(\sin^{-1}\)):
\[ \theta = \sin^{-1}\left(\frac{5}{8}\right) \]
Now, we can calculate \(\theta\):
\[ \theta \approx \sin^{-1}(0.625) \]
Using a calculator:
\[ \theta \approx 38.682 \text{ degrees} \]
Rounding this to the nearest whole degree:
\[ \theta \approx 39 \text{ degrees} \]
Therefore, the angle formed where the rope is fastened to the ground is approximately 39 degrees.