To find the distance \( x \) from the base of the ladder to the building, we can use trigonometric functions. Given the angle of elevation \( \theta \) is 46 degrees and the length of the ladder (hypotenuse) is 20 feet, we can use the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \( x \) (the distance from the base of the ladder to the building) is the adjacent side, and the hypotenuse is 20 feet.
\[ \cos(46^\circ) = \frac{x}{20} \]
Rearranging the equation to solve for \( x \):
\[ x = 20 \cdot \cos(46^\circ) \]
Now, we can calculate \( \cos(46^\circ) \) using a calculator:
\[ \cos(46^\circ) \approx 0.6947 \]
Now substitute this value back into the equation:
\[ x \approx 20 \cdot 0.6947 \approx 13.894 \text{ ft} \]
Rounding this to two decimal places gives:
\[ x \approx 13.89 \text{ ft} \]
Thus, the answer is:
A. x = 13.89 ft.
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