Final answer:
To determine the height of a man using a flagpole's shadow, we use proportional relationships between the height and shadow of the flagpole and the man. The proportion is height of flagpole/shadow of flagpole = height of man/shadow of man. Once we know the man's shadow length, at the same time of day, we can find his height.
Step-by-step explanation:
The student appears to be asking about how to determine the height of an object using the length of its shadow and a proportional relationship. We will use similar triangles here. The flagpole's height and shadow length create a right triangle with the ground. Assuming the light source (the Sun) is far enough away, similar objects will cast similar triangles, allowing us to use their relative proportions to determine unknown measurements.
If we have a 12 foot flagpole casting a 15 feet shadow, and we need to determine the height of a man standing next to the flagpole, we would use the proportion:
height of flagpole/shadow of flagpole = height of man/shadow of man
Substituting the known values, we have:
12 feet / 15 feet = height of man / shadow of man
This proportion can be used to find the unknown height of the man once his shadow length is measured at the same time of day, ensuring that the angle of the Sun's rays is consistent.