Question

Question
A telephone pole that is 14 ft. tall has fallen against a house. If the top of the telephone pole touches the house 8 ft. above the ground, what is the angle that the telephone pole makes with the ground?
(1 point)
Responses

29.7°
29.7°

55.2°
55.2°

60.3°
60.3°

34.8°
34.8°
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Answer 1

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°**