The shadow cast by a basketball hoop that is 10 feet high, next to Zion who is 55 feet tall and casts a 275-foot shadow, will be 50 feet long based on the calculations made using proportional relationships.
The student asked a question about the length of a shadow cast by a basketball hoop based on the shadow length of a nearby tall object. If Zion is 55 feet tall and casts a shadow of 275 feet, this indicates that there is a proportional relationship between the height of an object and the length of its shadow. To find the length of the shadow cast by a basketball hoop that is 10 feet high, we can set up a proportion since the sun's rays angle and the light conditions are assumed to be the same for both Zion and the basketball hoop.
The proportion is based on similar triangles created by the object and their shadows. We can write it as follows:
Zion's height / Zion's shadow length = Basketball hoop's height / Basketball hoop's shadow length
55 feet / 275 feet = 10 feet / x feet
Cross-multiplying to solve for 'x', we get:
55 * x = 275 * 10
x = (275 * 10) / 55
x = 50 feet
Therefore, the basketball hoop will cast a shadow of 50 feet.