Final answer:
Converting 1 mile to feet and using the tangent function gives the height of the building, rounded to the nearest foot, as approximately 1,022 feet.
Step-by-step explanation:
To find the height of the building, we use trigonometry. Specifically, we will utilize the concept of the angle of elevation and the tangent function.
The angle of elevation to the top of the building is given as 11°, and the distance from the observer to the base of the building is 1 mile, which we need to convert to feet.
First, we convert the distance to feet (1 mile = 5,280 feet).
The tangent of an angle in a right triangle is the ratio of the opposite side (height of the building in this case) over the adjacent side (the distance from the base of the building).
Thus, the formula will be: tan(11°) = height / 5,280 feet.
Solving for the height, we get:
height = tan(11°) × 5,280 feet.
Using a calculator, find tan(11°) and multiply by 5,280 feet to get the height in feet:
height = tan(11°) × 5,280 feet
≈ 1,022 feet.
Round to the nearest foot:
The height of the building is approximately 1,022 feet.