Final answer:
To approximate the height of the building, one can use the tangent trigonometric function by setting up a proportion with the given distance and angle of elevation, and then calculating the building's height accordingly.
Step-by-step explanation:
The student is asking how to approximate the height of a building given that they are standing 60 feet away and the angle of elevation to the top of the building is 41 degrees. To solve this, we utilize trigonometric functions, specifically the tangent function which relates angles to the opposite and adjacent sides of a right-angled triangle. Here's the step-by-step process to find the height of the building:
- Identify the given information: the distance from the building (adjacent side) is 60 feet, and the angle of elevation is 41 degrees.
- Recall the tangent function: tangent of angle = opposite side / adjacent side.
- Apply the formula: tangent(41 degrees) = building's height / 60 feet.
- Solve for the building's height: building's height = 60 feet * tangent(41 degrees).
- Calculate the height using a calculator to find the size of the tangent of 41 degrees.
This trigonometric method provides an approximation for the height of the building that can be compared against known measurements, as in the case of notable tall buildings or examples of scaling up from the height of a person.