the leaning tower of pisa is 55.9m tall and leans 5.5 deg from the vertical. if its shadow is 90.0m long, what is the distance from the top pf the tower to the edge of the shadow? assume that the ground is level.
please help in details
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.
To find the distance from the top of the leaning tower of Pisa to the edge of its shadow, we can use trigonometry.
First, let's define some terms:
- Height of the tower (h) = 55.9 meters
- Angle of inclination (θ) = 5.5 degrees
- Length of the shadow (s) = 90.0 meters
- Distance from the top of the tower to the edge of the shadow (d) - What we need to find
We are assuming the ground is level, so the distance from the base of the tower to the edge of the shadow is the same as the distance from the top of the tower to the edge of the shadow.
Now, let's use the tangent function to solve for "d":
tan(θ) = h / d
Rearranging this equation, we get:
d = h / tan(θ)
Substituting the given values into the equation:
d = 55.9 / tan(5.5)
Using a calculator, evaluate the tangent of 5.5 degrees (tan(5.5)) to get the value of 0.0968.
Now, substitute this value back into the equation:
d = 55.9 / 0.0968
Calculating the value of d by dividing 55.9 by 0.0968, we find:
d ≈ 576.55 meters
Therefore, the distance from the top of the leaning tower of Pisa to the edge of its shadow is approximately 576.55 meters.