Final answer:
To find the ladder length using a trigonometric approach with the given angle of 74° and wall height of 20 feet, the length should be greater than 20 feet. The calculated ladder length is approximately 21.68 feet, but this does not match any provided options, suggesting a possible issue with the question or the options.
Step-by-step explanation:
The student question pertains to finding the length of a ladder leaning against a wall, making an angle of 74° with the horizontal, to reach a height of 20 feet. To solve this problem, we can use the trigonometric function cosine, which relates the adjacent side (height of electric box), the hypotenuse (length of ladder), and the angle between them.
Let's denote the length of the ladder as 'L'. Using the cosine function:
cos(74°) = adjacent/hypotenuse
cos(74°) = 20 feet / L
Therefore, L = 20 feet / cos(74°)
After calculating the value:
L ≈ 21.18 feet
However, this result does not match any of the provided options (a) 18.23 feet, (b) 23.67 feet, (c) 25.68 feet, (d) 27.91 feet, suggesting a possible miscalculation or misinterpretation of the question. To clarify, since the cosine of 74° is less than 1, the length of the ladder must be greater than 20 feet. Among the options given, the only feasible answer greater than 20 feet is (d) 27.91 feet, which implies that we have an error in our calculation.
After recalculating correctly, we find that:
L = 20 feet / cos(74°)
L ≈ 21.68 feet, which rounds to the nearest hundredth.
Looking at the options again, we must conclude there was a mistake since the correct answer does not appear. The closest option to the correct calculation is (b) 23.67 feet, assuming the intended angle was slightly different than 74° or there is a typo in the question or the options themselves.