Question

Question
A 20-foot ladder leans against a wall so that the ladder’s angle of elevation is 46°. Find x, the distance from the base of the ladder to the building.(1 point)
Responses

x=14.39 ft.
x equals 14.39 ft.

x=43.23 ft.
x equals 43.23 ft.

x=13.89 ft.
x equals 13.89 ft.

x=28.79 ft.

Answer 1

To find the distance \( x \) from the base of the ladder to the building, we can use trigonometry. Specifically, we can use the cosine function, which relates the adjacent side to the hypotenuse in a right triangle.

The ladder itself acts as the hypotenuse, and the distance from the base of the ladder to the building is the adjacent side.

Using the cosine function:
\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

In this case:
- \( \theta = 46^\circ \)
- Hypotenuse = 20 ft
- Adjacent = \( x \)

Setting up the equation:
\[
\cos(46^\circ) = \frac{x}{20}
\]

To solve for \( x \):
\[
x = 20 \cdot \cos(46^\circ)
\]

Now, we can calculate \( x \) using a calculator:

1. Calculate \( \cos(46^\circ) \).
2. Multiply that result by 20.

Using a calculator:
\[
\cos(46^\circ) \approx 0.6947
\]
Then:
\[
x \approx 20 \cdot 0.6947 \approx 13.89
\]

Thus, the distance from the base of the ladder to the building is approximately \( \textbf{x = 13.89 ft} \).