Final answer:
To calculate the building's height, the tangent of the 10-degree angle of elevation is multiplied by the distance from the base, which is 5500 feet, giving an approximate height of 969.65 feet.
Step-by-step explanation:
To find the height of the building, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle. In this case, the angle of elevation is 10 degrees and the distance from the observer to the building is 5500 feet. The height of the building (opposite side) can be found with the formula:
height = distance × tan(angle of elevation)
We plug in the values to get:
height = 5500 feet × tan(10 degrees)
Using a calculator, we find that tan(10 degrees) ≈ 0.1763.
Therefore:
height ≈ 5500 × 0.1763
height ≈ 969.65 feet
So, the approximate height of the building is 969.65 feet.