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

• x = 28.79 ft.
• x = 43.23 ft.
• x = 14.39 ft.
• x = 13.89 ft.

Answer 1

To find the distance \( x \) from the base of the ladder to the building, we can use the cosine function from the angle of elevation:

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

Here, the hypotenuse is the length of the ladder (20 feet) and the adjacent side is the distance from the base of the ladder to the building (x).

Given:

• \( \theta = 46^\circ \)
• Length of the ladder (hypotenuse) = 20 feet

Using the cosine function:

\[ \cos(46^\circ) = \frac{x}{20} \]

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

\[ x = 20 \cdot \cos(46^\circ) \]

Calculating \( \cos(46^\circ) \):

\[ \cos(46^\circ) \approx 0.6947 \]

Now, substituting the value back in:

\[ x \approx 20 \cdot 0.6947 \approx 13.894 \]

Thus,

\[ x \approx 13.89 , \text{ft} \]

The correct answer is:

x = 13.89 ft.