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=13.89 ft.
x equals 13.89 ft.

x=28.79 ft.
x equals 28.79 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 building, we can use the trigonometric relationship based on the angle of elevation.

We have:

• The length of the ladder \( L = 20 \) feet,
• The angle of elevation \( \theta = 46^\circ \).

We can use the cosine function:

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

Rearranging for \( x \):

\[ x = L \cdot \cos(\theta) \]

Substituting in the values:

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

Now we calculate \( \cos(46^\circ) \):

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

Now plug that into the equation for \( x \):

\[ x \approx 20 \cdot 0.6947 \approx 13.894\text{ ft.} \]

Rounding this value gives:

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

Thus, the correct answer is:

x = 13.89 ft.