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

Answer 1

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

The formula we will use is:

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

In this case,

• \(\theta = 46^\circ\)
• The hypotenuse is the length of the ladder, which is 20 feet.
• The adjacent side is the distance we want to find (\( x \)).

Substituting the values into the formula:

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

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

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

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

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

Now plug this value back into the equation:

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

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

So the answer is \( x = 13.89 , \text{ft} \).