Math Problem Statement
Solution
This problem involves using proportional reasoning, since the shadow of a flagpole and a building are being compared under the same sunlight conditions. We can use the fact that the lengths of shadows are proportional to the heights of objects.
Known values:
- Shadow of the flagpole = 21 feet
- Shadow of the building = 54 feet
- Height of the building = 109 feet
We are trying to find the height of the flagpole, , using the ratio of height to shadow length:
Substitute the known values:
Now, solve for :
Thus, the approximate height of the flagpole is about 42 feet, which matches the second option.
Answer: 42 feet
Would you like more details on this? Here are a few related questions you could explore:
- How can we use proportions to solve other real-life problems?
- What would happen if the sun's angle changed? How would it affect the shadow lengths?
- Can this method of comparing shadows be applied to objects of any height?
- How would we calculate the height if we only knew the shadow lengths?
- Can we use trigonometry instead of proportions for shadow problems?
Tip:
Always make sure the conditions (like same time and place) for comparison in proportionality problems are consistent, otherwise the solution might not hold.
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Math Problem Analysis
Mathematical Concepts
Proportions
Ratios
Algebra
Formulas
height of flagpole / shadow of flagpole = height of building / shadow of building
Theorems
Proportionality Theorem
Suitable Grade Level
Grade 7