This is a right triangle trigonometry problem where we can use the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. In this case:

$\tan(28^\circ) = \frac{\text{height of the flagpole}}{\text{length of the shadow}} = \frac{h}{35 \, \text{feet}}$

To solve for $h$ (the height of the flagpole), we rearrange the equation:

$h = 35 \times \tan(28^\circ)$

Now, calculating the tangent of $28^\circ$:

$h = 35 \times 0.5317 \approx 18.61 \, \text{feet}$

So, the height of the flagpole is approximately 18.61 feet.

Would you like more details or have any questions about this solution?

Here are 5 related questions to consider:

1. How would the height change if the angle of elevation increased?
2. What is the length of the shadow if the height of the flagpole were doubled?
3. Can you use the sine or cosine function to solve for the height in this case?
4. What would happen to the shadow's length if the sun was at a higher elevation angle?
5. How do you calculate the angle of elevation given the height and the shadow length?

Tip: Always use the tangent function when you know the opposite and adjacent sides in a right triangle involving an angle.