Question

A 10 ft. ladder is resting against the wall. The ladder touches the ground 6 ft. away from the wall. What angle, rounded to the nearest tenth, is the bottom of the ladder making with the ground?
(1 point)
Responses

31.0°
31.0°

36.9°
36.9°

53.1°
53.1°

59.0°

Answer 1

To find the angle that the bottom of the ladder makes with the ground, we can use the sine, cosine, or tangent functions. In this scenario, we will use the cosine function, which relates the adjacent side and the hypotenuse in a right triangle.

In this case:
- The length of the ladder (hypotenuse) is 10 ft.
- The distance from the wall to the bottom of the ladder (adjacent side) is 6 ft.

We can use the cosine formula:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{6}{10}
\]

Calculating this gives:

\[
\cos(\theta) = 0.6
\]

To find the angle \(\theta\), we take the arccosine:

\[
\theta = \arccos(0.6)
\]

Using a calculator to find the angle:

\[
\theta \approx 53.1°
\]

Therefore, the angle that the bottom of the ladder makes with the ground, rounded to the nearest tenth, is **53.1°**.