Final answer:
Using the properties of similar triangles, where the man's height to shadow ratio is proportional to the Ferris wheel's height to shadow ratio, the height of the Ferris wheel's shadow when the man's height is 18 meters and his shadow is 24 meters, is calculated to be 15 meters.
Step-by-step explanation:
Similar Triangles to Solve for the Ferris Wheel's Height
The problem at hand involves finding the height of a Ferris wheel using the properties of similar triangles. When a Ferris wheel casts a 20-meter shadow while at the same time a man 18 meters tall casts a 24-meter shadow, we can use the comparison of these two situations to determine the height of the Ferris wheel. We apply the concept that corresponding sides of similar triangles are proportional.
Let h represent the height of the Ferris wheel. We then set up a proportion based on the similar triangles formed by the objects and their shadows:
- Man's height / Man's shadow = Ferris wheel's height / Ferris wheel's shadow
- 18 m / 24 m = h / 20 m
Solving for h gives us:
18 m / 24 m = h / 20 m
By cross-multiplication, we get:
18 m * 20 m = h * 24 m
Therefore, h = (18 m * 20 m) / 24 m
h = 15 m
The height of the Ferris wheel's shadow, when the man standing next to it has an 18-meter height and casts a 24-meter shadow, is 15 meters.