Final answer:
Using trigonometry and the tangent function, the distance from the observer to the top of the 80-foot building at a 52° angle of elevation is calculated to be approximately 63.66 feet. This distance is not listed in the provided options, suggesting an error or an issue with the provided options.
Step-by-step explanation:
To determine the distance from the observer to the top of the building when the building is 80 feet tall and the angle of elevation is 52°, we can use trigonometry. Specifically, we'll apply the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. Here, the opposite side is the height of the building, and the adjacent side is what we're trying to find.
We have tangent of 52° = opposite side / adjacent side, or tan(52°) = 80 / distance. Now we solve for distance: distance = 80 / tan(52°). When calculated, this gives us a distance of approximately 63.66 feet, which isn't an option provided. Therefore, we should reevaluate our approach to ensure there were no calculation errors. If the calculation is correct, the correct answer may not be listed, and it would be advised to double-check the question and options.