Final answer:
Using the tangent function from trigonometry, the estimated distance to the base of a building with a height of 450ft and an angle of elevation of 22° is approximately 1114 feet.
Step-by-step explanation:
The task is to use trigonometry to estimate the distance to the base of the building when the angle of elevation and the building's height are known. In this scenario, an angle of elevation of 22° to a building that is 450ft tall is given.
To find the distance to the building, we can use the tangent function (tan) in trigonometry, which relates the angle of elevation to the opposite side (height of the building) and adjacent side (distance to the building) in a right-angled triangle. The formula to determine the distance to the building (d) is:
d = height / tan(angle)
Substituting the given values:
d = 450ft / tan(22°)
Using a calculator, find the tangent of 22°, then divide the height of the building by this value to get the distance.
The estimated distance to the base of the building would be:
d ≈ 450ft / 0.4040 ≈ 1113.86 ft
Therefore, the estimated distance from the observer to the base of the building is approximately 1114 feet.