Final answer:
To calculate the height of the building, the tangent of the 68° angle of elevation is used, with the distance of 120 feet from the building as the adjacent side in the trigonometric ratio formula. Multiplying the tangent of 68° by 120 feet gives the building's height, which is then rounded to the nearest foot to match one of the given options.
Step-by-step explanation:
The question asks for the height of a building given that from a point 120 feet away at ground level, the angle of elevation to the top of the building is 68°. To solve this problem, we can use trigonometric relationships, specifically the tangent of the angle of elevation, which is the ratio of the opposite side (height of the building) to the adjacent side (distance from the building).
Using the formula tangent(angle) = opposite/adjacent, we can write tangent(68°) = height/120 feet. To find the height, we rearrange the formula to height = 120 feet × tangent(68°).
After calculating the tangent of 68° and multiplying by 120 feet, we can round to the nearest foot to find the height of the building. The correct height to the nearest foot must be one of the options given: A. 108 feet, B. 58 feet, C. 92 feet, or D. 176 feet.