Final answer:
The height of the Empire State Building can be calculated using the tangent of the angle of elevation. With an angle of 11° and a distance of 1 mile from the building, the height is approximately 1027 feet.
Step-by-step explanation:
To find the height of the Empire State Building using the angle of elevation, we can apply trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the building here) and the adjacent side (the distance from the building). The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side (tan(angle) = opposite/adjacent).
Given:
Angle of elevation = 11°
Distance from the building = 1 mile (we will convert this to feet to match the height of the building in feet)
Step 1: Convert 1 mile to feet
1 mile = 5280 feet.
Step 2: Use the tangent function
tan(11°) = height / 5280 feet.
Step 3: Solve for the height
height = tan(11°) × 5280 feet.
height = 0.19438 × 5280 feet.
height = approximately 1027 feet.