To find the angle that the fallen telephone pole makes with the ground, we can use some basic trigonometry. We'll visualize this scenario and identify a right triangle formed by the following:
- The height at which the top of the telephone pole touches the house (8 ft) represents one side (opposite) of the triangle.
- The height of the telephone pole (14 ft) represents the length of the pole (hypotenuse).
- The angle θ is the angle between the ground and the telephone pole.
We can use the sine function, which relates the opposite side to the hypotenuse:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Here:
- Opposite = 8 ft
- Hypotenuse = 14 ft
Plugging in the values:
\[ \sin(\theta) = \frac{8}{14} = \frac{4}{7} \]
Now, we can find θ by taking the inverse sine (arcsin) of \(\frac{4}{7}\):
\[ \theta = \arcsin\left(\frac{4}{7}\right) \]
Using a calculator to find the angle:
\[ \theta \approx 29.7° \]
Thus, the angle that the telephone pole makes with the ground is approximately 29.7°.
So the answer is:
29.7°