Final answer:
Using trigonometry, the height of the building is calculated as approximately 18.1 feet, which does not match any of the provided multiple-choice options. This indicates a potential discrepancy that may need to be resolved either in the options or the calculation itself.
Step-by-step explanation:
To determine the height of the building, we will use trigonometry. The shadow of the building and the angle of elevation form a right triangle with the building's height as one of the sides.
The tangent of an angle in a right triangle relates the opposite side to the adjacent side, so we have:
tangent(35°) = opposite / adjacent
tangent(35°) = height of the building / 26 feet
Using the tangent function, we find
height of the building = tangent(35°) * 26 feet
Next, we calculate the height:
height of the building = 0.7002 * 26 feet ≈ 18.2 feet
However, since 18.2 feet is not one of the multiple-choice options provided, we must reevaluate our answer. Checking the calculation process for errors, we realize this was a rounding error. The correct calculation is
height of the building ≈ 18.1 feet
As such, none of the choices (a) 14.1 feet, (b) 28.2 feet, (c) 30.5 feet, (d) 35.8 feet, matches our calculated height. It's possible there's an error in the question choices or a mistake in the calculation that needs to be addressed.