To solve this problem, we can use trigonometry. We know the height of the leaning tower, the angle of inclination, and the length of its shadow. We can use these values to find the distance from the top of the tower to the edge of the shadow.
Let's break down the given information:
Height of the leaning tower (h): 55.9m
Angle of inclination (θ): 5.5 degrees
Shadow length (s): 90.0m
Now, we can use the tangent function (tan) to determine the distance from the top of the tower to the edge of the shadow. The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the tower, and the adjacent side is the distance we want to find.
Let's set up the equation:
tan(θ) = h / x
Rearranging the equation to solve for x:
x = h / tan(θ)
Substituting the known values:
x = 55.9 / tan(5.5)
Using a calculator, we can find the tangent of 5.5 degrees:
tan(5.5) ≈ 0.09602
Now, we can substitute this value into the equation:
x = 55.9 / 0.09602 ≈ 582.36
Therefore, the distance from the top of the leaning tower of Pisa to the edge of its shadow is approximately 582.36 meters.