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 = 14.39 ft

x = 43.23 ft
x = 43.23 ft

x = 13.89 ft
x = 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 the cosine function in trigonometry.

The cosine of the angle of elevation is given by the formula:

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

In this case:
- \( \theta = 46^\circ \)
- The hypotenuse (length of the ladder) is 20 feet.
- The adjacent side is the distance \( x \).

Rearranging the formula gives:

\[
x = \text{hypotenuse} \cdot \cos(\theta) = 20 \cdot \cos(46^\circ)
\]

Now, calculating \( x \):

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

Using a calculator to find \( \cos(46^\circ) \):

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

Now substitute this value in:

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

So, \( x \approx 13.89 \) ft.

Thus, the correct answer is:

**x = 13.89 ft**