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, $h$, using the ratio of height to shadow length:

$\frac{\text{Height of flagpole}}{\text{Shadow of flagpole}} = \frac{\text{Height of building}}{\text{Shadow of building}}$

Substitute the known values:

$\frac{h}{21} = \frac{109}{54}$

Now, solve for $h$:

$h = \frac{109 \times 21}{54}$

$h \approx \frac{2289}{54} = 42.39$

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:

1. How can we use proportions to solve other real-life problems?
2. What would happen if the sun's angle changed? How would it affect the shadow lengths?
3. Can this method of comparing shadows be applied to objects of any height?
4. How would we calculate the height if we only knew the shadow lengths?
5. 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.