Final answer:
Using the tangent function with the given angle of elevation (70 degrees) and the height of the Statue of Liberty (305 feet), we can calculate the distance from Allison to the base of the statue by dividing the height by the tangent of the angle.
Step-by-step explanation:
The question asks for the distance between Allison and the base of the Statue of Liberty, given the angle of elevation and the height of the Statue. We can solve this problem using trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (statue's height) and the adjacent side (distance from the base).
The tangent of the angle of elevation (70°) is equal to the opposite side (statue's height of 305 feet) divided by the adjacent side (distance from the base), which we are trying to find:
tan(70°) = 305 feet / distance from the base
To find the distance from the base, we simply rearrange the equation and solve for the distance:
distance from the base = 305 feet / tan(70°)
Once we calculate this using a calculator, we will have the answer to the problem