Final answer:
Using trigonometry with the given angle of 74 degrees to reach a height of 22 feet, the ladder's length can be calculated. However, the calculated length of approximately 23.27 feet does not match any of the given options, indicating a potential discrepancy in the question or the options provided.
Step-by-step explanation:
To find the length of the ladder that an electrician leans against a house at a 74° angle to reach an electric box 22 feet up, we can use trigonometry. Specifically, the cosine of the angle will give us the ratio of the adjacent side over the hypotenuse. The adjacent side is the distance up the wall to the electric box, and we need to find the hypotenuse, which is the length of the ladder.
Using the formula:
cos(74°) = Adjacent / Hypotenuse
We plug in the values:
cos(74°) = 22 / Hypotenuse
To solve for the hypotenuse (the length of the ladder), we rearrange:
Hypotenuse = 22 / cos(74°)
Calculating this gives:
Hypotenuse ≈ 22 / cos(74°) ≈ 23.27 feet
This is not an option listed, implying there might be a miscalculation or a typo in either the angles, the height, or the options provided. The nearest option to our result is (d) 27.91 feet, but this does not match our calculation.