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)

Question

Responses

x=28.79 ft.
𝑥
=
28.79

ft.
x equals 28.79 ft.

x=13.89 ft.
𝑥
=
13.89

ft.
x equals 13.89 ft.

x=14.39 ft.
𝑥
=
14.39

ft.
x equals 14.39 ft.

x=43.23 ft.

Answer 1

To find the distance \( x \) from the base of the ladder to the wall, we can use basic trigonometry. We know that the ladder forms a right triangle with the wall, where:

• The length of the ladder is the hypotenuse, which is 20 feet.
• The angle of elevation to the top of the ladder is 46°.
• The distance from the base of the ladder to the wall is the adjacent side.

Using the cosine function:

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

Substituting the known values:

\[ \cos(46°) = \frac{x}{20} \]

Now, we can solve for \( x \):

\[ x = 20 \cdot \cos(46°) \]

Calculating \( \cos(46°) \):

\[ \cos(46°) \approx 0.6947 \]

Now substitute this value into the equation:

\[ x \approx 20 \cdot 0.6947 \approx 13.89 \]

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

So the correct response is:

x = 13.89 ft.