Final answer:
Using trigonometry and the tangent function, the height of the building is calculated to be approximately 65.385 feet. After rounding, the building's height is 65 feet.
Step-by-step explanation:
To find the height of the building, we 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 depression to the car is given as 36 degrees, and the distance from the car to the base of the building (adjacent side) is 90 feet.
To find the height of the building (opposite side), we set up the following equation using the tangent of 36 degrees:
tan(36°) = height / 90 feet
Next, we solve for the height by multiplying both sides of the equation by 90 feet:
height = 90 feet * tan(36°)
After calculating the tangent of 36 degrees and multiplying by 90, we find that the height of the building is approximately:
height ≈ 90 feet * 0.7265
height ≈ 65.385 feet
Rounding to the nearest whole number, the height of the building is 65 feet.