To find the distance along the ground from the base of the ladder to the wall (the horizontal distance), we will be using the cosine function. The cosine of an angle in a right triangle is defined as the length of the adjacent side (the horizontal distance from the base of the ladder to the wall) divided by the length of the hypotenuse (the length of the ladder).
Given:
- The angle of elevation is 46°.
- The length of the ladder (hypotenuse) is 20 feet.
Using the cosine function, we can set up the following equation:
\[ \cos(46°) = \frac{x}{20} \]
Where \(x\) is the distance from the base of the ladder to the wall.
This equation can be rearranged to solve for \(x\):
\[ x = 20 \cdot \cos(46°) \]
So, the correct option to use for this setup is Option #2: cos(46°) = x/20.
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